1648116336

# How To Improve Brand Communication Strategy. Essential Tips

Brand communication strategy is one of the most crucial aspects of a business that many people fail to incorporate. So, what is brand communication? In short, a brand communication strategy can be defined as a method through which you use communication to obtain your desired goals and outcomes. It is essential to all brands as it is the primary medium that will link you to success.

Through these strategies, you will have the ability to enlighten your stakeholders about your brand and speak about its products, services, strengths, values, and so on. In a nutshell, this will dictate what people hear and think about your brand itself and all that it offers:

https://simply-contact.com/improve-brand-communication-strategy/

1679035563

## How to Add Splash Screen in Android and iOS with Flutter

When your app is opened, there is a brief time while the native app loads Flutter. By default, during this time, the native app displays a white splash screen. This package automatically generates iOS, Android, and Web-native code for customizing this native splash screen background color and splash image. Supports dark mode, full screen, and platform-specific options.

## What's New

[BETA] Support for flavors is in beta. Currently only Android and iOS are supported. See instructions below.

You can now keep the splash screen up while your app initializes! No need for a secondary splash screen anymore. Just use the preserve and remove methods together to remove the splash screen after your initialization is complete. See details below.

## Usage

Would you prefer a video tutorial instead? Check out Johannes Milke's tutorial.

First, add flutter_native_splash as a dependency in your pubspec.yaml file.

dependencies:
flutter_native_splash: ^2.2.19


Don't forget to flutter pub get.

### 1. Setting the splash screen

Customize the following settings and add to your project's pubspec.yaml file or place in a new file in your root project folder named flutter_native_splash.yaml.

flutter_native_splash:
# This package generates native code to customize Flutter's default white native splash screen
# with background color and splash image.
# Customize the parameters below, and run the following command in the terminal:
# flutter pub run flutter_native_splash:create
# To restore Flutter's default white splash screen, run the following command in the terminal:
# flutter pub run flutter_native_splash:remove

# color or background_image is the only required parameter.  Use color to set the background
# of your splash screen to a solid color.  Use background_image to set the background of your
# splash screen to a png image.  This is useful for gradients. The image will be stretch to the
# size of the app. Only one parameter can be used, color and background_image cannot both be set.
color: "#42a5f5"
#background_image: "assets/background.png"

# Optional parameters are listed below.  To enable a parameter, uncomment the line by removing

# The image parameter allows you to specify an image used in the splash screen.  It must be a
# png file and should be sized for 4x pixel density.
#image: assets/splash.png

# The branding property allows you to specify an image used as branding in the splash screen.
# It must be a png file. It is supported for Android, iOS and the Web.  For Android 12,
# see the Android 12 section below.
#branding: assets/dart.png

# To position the branding image at the bottom of the screen you can use bottom, bottomRight,
# and bottomLeft. The default values is bottom if not specified or specified something else.
#branding_mode: bottom

# The color_dark, background_image_dark, image_dark, branding_dark are parameters that set the background
# and image when the device is in dark mode. If they are not specified, the app will use the
# parameters from above. If the image_dark parameter is specified, color_dark or
# background_image_dark must be specified.  color_dark and background_image_dark cannot both be
# set.
#color_dark: "#042a49"
#background_image_dark: "assets/dark-background.png"
#image_dark: assets/splash-invert.png
#branding_dark: assets/dart_dark.png

# Android 12 handles the splash screen differently than previous versions.  Please visit
# https://developer.android.com/guide/topics/ui/splash-screen
# Following are Android 12 specific parameter.
android_12:
# The image parameter sets the splash screen icon image.  If this parameter is not specified,
# the app's launcher icon will be used instead.
# Please note that the splash screen will be clipped to a circle on the center of the screen.
# App icon with an icon background: This should be 960×960 pixels, and fit within a circle
# 640 pixels in diameter.
# App icon without an icon background: This should be 1152×1152 pixels, and fit within a circle
# 768 pixels in diameter.
#image: assets/android12splash.png

# Splash screen background color.
#color: "#42a5f5"

# App icon background color.
#icon_background_color: "#111111"

# The branding property allows you to specify an image used as branding in the splash screen.
#branding: assets/dart.png

# The image_dark, color_dark, icon_background_color_dark, and branding_dark set values that
# apply when the device is in dark mode. If they are not specified, the app will use the
# parameters from above.
#image_dark: assets/android12splash-invert.png
#color_dark: "#042a49"
#icon_background_color_dark: "#eeeeee"

# The android, ios and web parameters can be used to disable generating a splash screen on a given
# platform.
#android: false
#ios: false
#web: false

# Platform specific images can be specified with the following parameters, which will override
# the respective parameter.  You may specify all, selected, or none of these parameters:
#color_android: "#42a5f5"
#color_dark_android: "#042a49"
#color_ios: "#42a5f5"
#color_dark_ios: "#042a49"
#color_web: "#42a5f5"
#color_dark_web: "#042a49"
#image_android: assets/splash-android.png
#image_dark_android: assets/splash-invert-android.png
#image_ios: assets/splash-ios.png
#image_dark_ios: assets/splash-invert-ios.png
#image_web: assets/splash-web.png
#image_dark_web: assets/splash-invert-web.png
#background_image_android: "assets/background-android.png"
#background_image_dark_android: "assets/dark-background-android.png"
#background_image_ios: "assets/background-ios.png"
#background_image_dark_ios: "assets/dark-background-ios.png"
#background_image_web: "assets/background-web.png"
#background_image_dark_web: "assets/dark-background-web.png"
#branding_android: assets/brand-android.png
#branding_dark_android: assets/dart_dark-android.png
#branding_ios: assets/brand-ios.png
#branding_dark_ios: assets/dart_dark-ios.png

# The position of the splash image can be set with android_gravity, ios_content_mode, and
# web_image_mode parameters.  All default to center.
#
# android_gravity can be one of the following Android Gravity (see
# https://developer.android.com/reference/android/view/Gravity): bottom, center,
# center_horizontal, center_vertical, clip_horizontal, clip_vertical, end, fill, fill_horizontal,
# fill_vertical, left, right, start, or top.
#android_gravity: center
#
# ios_content_mode can be one of the following iOS UIView.ContentMode (see
# https://developer.apple.com/documentation/uikit/uiview/contentmode): scaleToFill,
# scaleAspectFit, scaleAspectFill, center, top, bottom, left, right, topLeft, topRight,
# bottomLeft, or bottomRight.
#ios_content_mode: center
#
# web_image_mode can be one of the following modes: center, contain, stretch, and cover.
#web_image_mode: center

# The screen orientation can be set in Android with the android_screen_orientation parameter.
# Valid parameters can be found here:
# https://developer.android.com/guide/topics/manifest/activity-element#screen
#android_screen_orientation: sensorLandscape

# To hide the notification bar, use the fullscreen parameter.  Has no effect in web since web
# has no notification bar.  Defaults to false.
# NOTE: Unlike Android, iOS will not automatically show the notification bar when the app loads.
#       WidgetsFlutterBinding.ensureInitialized();
#       SystemChrome.setEnabledSystemUIOverlays([SystemUiOverlay.bottom, SystemUiOverlay.top]);
#fullscreen: true

# If you have changed the name(s) of your info.plist file(s), you can specify the filename(s)
# with the info_plist_files parameter.  Remove only the # characters in the three lines below,
# do not remove any spaces:
#info_plist_files:
#  - 'ios/Runner/Info-Debug.plist'
#  - 'ios/Runner/Info-Release.plist'


### 2. Run the package

flutter pub run flutter_native_splash:create


To specify the YAML file location just add --path with the command in the terminal:

flutter pub run flutter_native_splash:create --path=path/to/my/file.yaml


### 3. Set up app initialization (optional)

By default, the splash screen will be removed when Flutter has drawn the first frame. If you would like the splash screen to remain while your app initializes, you can use the preserve() and remove() methods together. Pass the preserve() method the value returned from WidgetsFlutterBinding.ensureInitialized() to keep the splash on screen. Later, when your app has initialized, make a call to remove() to remove the splash screen.

import 'package:flutter_native_splash/flutter_native_splash.dart';

void main() {
WidgetsBinding widgetsBinding = WidgetsFlutterBinding.ensureInitialized();
FlutterNativeSplash.preserve(widgetsBinding: widgetsBinding);
runApp(const MyApp());
}

// whenever your initialization is completed, remove the splash screen:
FlutterNativeSplash.remove();


NOTE: If you do not need to use the preserve() and remove() methods, you can place the flutter_native_splash dependency in the dev_dependencies section of pubspec.yaml.

### 4. Support the package (optional)

If you find this package useful, you can support it for free by giving it a thumbs up at the top of this page. Here's another option to support the package:

## Android 12+ Support

Android 12 has a new method of adding splash screens, which consists of a window background, icon, and the icon background. Note that a background image is not supported.

Be aware of the following considerations regarding these elements:

1: image parameter. By default, the launcher icon is used:

• App icon without an icon background, as shown on the left: This should be 1152×1152 pixels, and fit within a circle 768 pixels in diameter.
• App icon with an icon background, as shown on the right: This should be 960×960 pixels, and fit within a circle 640 pixels in diameter.

2: icon_background_color is optional, and is useful if you need more contrast between the icon and the window background.

3: One-third of the foreground is masked.

4: color the window background consists of a single opaque color.

PLEASE NOTE: The splash screen may not appear when you launch the app from Android Studio on API 31. However, it should appear when you launch by clicking on the launch icon in Android. This seems to be resolved in API 32+.

PLEASE NOTE: There are a number of reports that non-Google launchers do not display the launch image correctly. If the launch image does not display correctly, please try the Google launcher to confirm that this package is working.

PLEASE NOTE: The splash screen does not appear when you launch the app from a notification. Apparently this is the intended behavior on Android 12: core-splashscreen Icon not shown when cold launched from notification.

## Flavor Support

If you have a project setup that contains multiple flavors or environments, and you created more than one flavor this would be a feature for you.

Instead of maintaining multiple files and copy/pasting images, you can now, using this tool, create different splash screens for different environments.

### Pre-requirements

In order to use the new feature, and generate the desired splash images for you app, a couple of changes are required.

If you want to generate just one flavor and one file you would use either options as described in Step 1. But in order to setup the flavors, you will then be required to move all your setup values to the flutter_native_splash.yaml file, but with a prefix.

Let's assume for the rest of the setup that you have 3 different flavors, Production, Acceptance, Development.

First this you will need to do is to create a different setup file for all 3 flavors with a suffix like so:

flutter_native_splash-production.yaml
flutter_native_splash-acceptance.yaml
flutter_native_splash-development.yaml


You would setup those 3 files the same way as you would the one, but with different assets depending on which environment you would be generating. For example (Note: these are just examples, you can use whatever setup you need for your project that is already supported by the package):

# flutter_native_splash-development.yaml
flutter_native_splash:
color: "#ffffff"
image: assets/logo-development.png
branding: assets/branding-development.png
color_dark: "#121212"
image_dark: assets/logo-development.png
branding_dark: assets/branding-development.png

android_12:
image: assets/logo-development.png
icon_background_color: "#ffffff"
image_dark: assets/logo-development.png
icon_background_color_dark: "#121212"

web: false

# flutter_native_splash-acceptance.yaml
flutter_native_splash:
color: "#ffffff"
image: assets/logo-acceptance.png
branding: assets/branding-acceptance.png
color_dark: "#121212"
image_dark: assets/logo-acceptance.png
branding_dark: assets/branding-acceptance.png

android_12:
image: assets/logo-acceptance.png
icon_background_color: "#ffffff"
image_dark: assets/logo-acceptance.png
icon_background_color_dark: "#121212"

web: false

# flutter_native_splash-production.yaml
flutter_native_splash:
color: "#ffffff"
image: assets/logo-production.png
branding: assets/branding-production.png
color_dark: "#121212"
image_dark: assets/logo-production.png
branding_dark: assets/branding-production.png

android_12:
image: assets/logo-production.png
icon_background_color: "#ffffff"
image_dark: assets/logo-production.png
icon_background_color_dark: "#121212"

web: false


Great, now comes the fun part running the new command!

The new command is:

# If you have a flavor called production you would do this:
flutter pub run flutter_native_splash:create --flavor production

# For a flavor with a name staging you would provide it's name like so:
flutter pub run flutter_native_splash:create --flavor staging

# And if you have a local version for devs you could do that:
flutter pub run flutter_native_splash:create --flavor development


### Android setup

You're done! No, really, Android doesn't need any additional setup.

Note: If it didn't work, please make sure that your flavors are named the same as your config files, otherwise the setup will not work.

### iOS setup

iOS is a bit tricky, so hang tight, it might look scary but most of the steps are just a single click, explained as much as possible to lower the possibility of mistakes.

When you run the new command, you will need to open xCode and follow the steps bellow:

Assumption

• In order for this setup to work, you would already have 3 different schemes setup; production, acceptance and development.

Preparation

• Open the iOS Flutter project in Xcode (open the Runner.xcworkspace)
• Find the newly created Storyboard files at the same location where the original is {project root}/ios/Runner/Base.lproj
• Select all of them and drag and drop into Xcode, directly to the left hand side where the current LaunchScreen.storyboard is located already
• After you drop your files there Xcode will ask you to link them, make sure you select 'Copy if needed'
• This part is done, you have linked the newly created storyboards in your project.

xCode

Xcode still doesn't know how to use them, so we need to specify for all the current flavors (schemes) which file to use and to use that value inside the Info.plist file.

• Open the iOS Flutter project in Xcode (open the Runner.xcworkspace)
• Click the Runner project in the top left corner (usually the first item in the list)
• In the middle part of the screen, on the left side, select the Runner target
• On the top part of the screen select Build Settings
• Make sure that 'All' and 'Combined' are selected
• Next to 'Combine' you have a '+' button, press it and select 'Add User-Defined Setting'
• Once you do that Xcode will create a new variable for you to name. Suggestion is to name it LAUNCH_SCREEN_STORYBOARD
• Once you do that, you will have the option to define a specific name for each flavor (scheme) that you have defined in the project. Make sure that you input the exact name of the LaunchScreen.storyboard that was created by this tool
• Example: If you have a flavor Development, there is a Storyboard created name LaunchScreenDevelopment.storyboard, please add that name (without the storyboard part) to the variable value next to the flavor value
• After you finish with that, you need to update Info.plist file to link the newly created variable so that it's used correctly
• Open the Info.plist file
• Find the entry called 'Launch screen interface file base name'
• The default value is 'LaunchScreen', change that to the variable name that you create previously. If you follow these steps exactly, it would be LAUNCH_SCREEN_STORYBOARD, so input this $(LAUNCH_SCREEN_STORYBOARD) • And your done! Congrats you finished your setup for multiple flavors, ## FAQs ### I got the error "A splash screen was provided to Flutter, but this is deprecated." This message is not related to this package but is related to a change in how Flutter handles splash screens in Flutter 2.5. It is caused by having the following code in your android/app/src/main/AndroidManifest.xml, which was included by default in previous versions of Flutter: <meta-data android:name="io.flutter.embedding.android.SplashScreenDrawable" android:resource="@drawable/launch_background" />  The solution is to remove the above code. Note that this will also remove the fade effect between the native splash screen and your app. ### Are animations/lottie/GIF images supported? Not at this time. PRs are always welcome! ### I got the error AAPT: error: style attribute 'android:attr/windowSplashScreenBackground' not found This attribute is only found in Android 12, so if you are getting this error, it means your project is not fully set up for Android 12. Did you update your app's build configuration? ## I see a flash of the wrong splash screen on iOS This is caused by an iOS splash caching bug, which can be solved by uninstalling your app, powering off your device, power back on, and then try reinstalling. ## I see a white screen between splash screen and app 1. It may be caused by an iOS splash caching bug, which can be solved by uninstalling your app, powering off your device, power back on, and then try reinstalling. 2. It may be caused by the delay due to initialization in your app. To solve this, put any initialization code in the removeAfter method. ### Can I base light/dark mode on app settings? No. This package creates a splash screen that is displayed before Flutter is loaded. Because of this, when the splash screen loads, internal app settings are not available to the splash screen. Unfortunately, this means that it is impossible to control light/dark settings of the splash from app settings. Notes If the splash screen was not updated correctly on iOS or if you experience a white screen before the splash screen, run flutter clean and recompile your app. If that does not solve the problem, delete your app, power down the device, power up the device, install and launch the app as per this StackOverflow thread. This package modifies launch_background.xml and styles.xml files on Android, LaunchScreen.storyboard and Info.plist on iOS, and index.html on Web. If you have modified these files manually, this plugin may not work properly. Please open an issue if you find any bugs. ## How it works ### Android • Your splash image will be resized to mdpi, hdpi, xhdpi, xxhdpi and xxxhdpi drawables. • An <item> tag containing a <bitmap> for your splash image drawable will be added in launch_background.xml • Background color will be added in colors.xml and referenced in launch_background.xml. • Code for full screen mode toggle will be added in styles.xml. • Dark mode variants are placed in drawable-night, values-night, etc. resource folders. ### iOS • Your splash image will be resized to @3x and @2x images. • Color and image properties will be inserted in LaunchScreen.storyboard. • The background color is implemented by using a single-pixel png file and stretching it to fit the screen. • Code for hidden status bar toggle will be added in Info.plist. ### Web • A web/splash folder will be created for splash screen images and CSS files. • Your splash image will be resized to 1x, 2x, 3x, and 4x sizes and placed in web/splash/img. • The splash style sheet will be added to the app's web/index.html, as well as the HTML for the splash pictures. ## Acknowledgments This package was originally created by Henrique Arthur and it is currently maintained by Jon Hanson. ## Bugs or Requests If you encounter any problems feel free to open an issue. If you feel the library is missing a feature, please raise a ticket. Pull request are also welcome. ## Use this package as a library ### Depend on it Run this command: With Flutter: $ flutter pub add flutter_native_splash

This will add a line like this to your package's pubspec.yaml (and run an implicit flutter pub get):

dependencies:
flutter_native_splash: ^2.2.19

Alternatively, your editor might support flutter pub get. Check the docs for your editor to learn more.

### Import it

Now in your Dart code, you can use:

import 'package:flutter_native_splash/flutter_native_splash.dart';

## example/lib/main.dart

import 'package:flutter/material.dart';
import 'package:flutter_native_splash/flutter_native_splash.dart';

void main() {
WidgetsBinding widgetsBinding = WidgetsFlutterBinding.ensureInitialized();
FlutterNativeSplash.preserve(widgetsBinding: widgetsBinding);
runApp(const MyApp());
}

class MyApp extends StatelessWidget {
const MyApp({super.key});

// This widget is the root of your application.
@override
Widget build(BuildContext context) {
return MaterialApp(
title: 'Flutter Demo',
theme: ThemeData(
// This is the theme of your application.
//
// Try running your application with "flutter run". You'll see the
// application has a blue toolbar. Then, without quitting the app, try
// changing the primarySwatch below to Colors.green and then invoke
// "hot reload" (press "r" in the console where you ran "flutter run",
// or simply save your changes to "hot reload" in a Flutter IDE).
// Notice that the counter didn't reset back to zero; the application
// is not restarted.
primarySwatch: Colors.blue,
),
);
}
}

class MyHomePage extends StatefulWidget {
const MyHomePage({super.key, required this.title});

// that it has a State object (defined below) that contains fields that affect
// how it looks.

// This class is the configuration for the state. It holds the values (in this
// case the title) provided by the parent (in this case the App widget) and
// used by the build method of the State. Fields in a Widget subclass are
// always marked "final".

final String title;

@override
State<MyHomePage> createState() => _MyHomePageState();
}

class _MyHomePageState extends State<MyHomePage> {
int _counter = 0;

void _incrementCounter() {
setState(() {
// This call to setState tells the Flutter framework that something has
// changed in this State, which causes it to rerun the build method below
// so that the display can reflect the updated values. If we changed
// _counter without calling setState(), then the build method would not be
// called again, and so nothing would appear to happen.
_counter++;
});
}

@override
void initState() {
super.initState();
initialization();
}

void initialization() async {
// This is where you can initialize the resources needed by your app while
// the splash screen is displayed.  Remove the following example because
// delaying the user experience is a bad design practice!
// ignore_for_file: avoid_print
await Future.delayed(const Duration(seconds: 1));
await Future.delayed(const Duration(seconds: 1));
await Future.delayed(const Duration(seconds: 1));
print('go!');
FlutterNativeSplash.remove();
}

@override
Widget build(BuildContext context) {
// This method is rerun every time setState is called, for instance as done
// by the _incrementCounter method above.
//
// The Flutter framework has been optimized to make rerunning build methods
// fast, so that you can just rebuild anything that needs updating rather
// than having to individually change instances of widgets.
return Scaffold(
appBar: AppBar(
// Here we take the value from the MyHomePage object that was created by
// the App.build method, and use it to set our appbar title.
title: Text(widget.title),
),
body: Center(
// Center is a layout widget. It takes a single child and positions it
// in the middle of the parent.
child: Column(
// Column is also a layout widget. It takes a list of children and
// arranges them vertically. By default, it sizes itself to fit its
// children horizontally, and tries to be as tall as its parent.
//
// Invoke "debug painting" (press "p" in the console, choose the
// "Toggle Debug Paint" action from the Flutter Inspector in Android
// Studio, or the "Toggle Debug Paint" command in Visual Studio Code)
// to see the wireframe for each widget.
//
// Column has various properties to control how it sizes itself and
// how it positions its children. Here we use mainAxisAlignment to
// center the children vertically; the main axis here is the vertical
// axis because Columns are vertical (the cross axis would be
// horizontal).
mainAxisAlignment: MainAxisAlignment.center,
children: <Widget>[
const Text(
'You have pushed the button this many times:',
),
Text(
'$_counter', style: Theme.of(context).textTheme.headlineMedium, ), ], ), ), floatingActionButton: FloatingActionButton( onPressed: _incrementCounter, tooltip: 'Increment', child: const Icon(Icons.add), ), // This trailing comma makes auto-formatting nicer for build methods. ); } }  ## Download Details: Author: jonbhanson Download Link: Download The Source Code Official Website: https://github.com/jonbhanson/flutter_native_splash License: MIT license 1624879756 ## Employer Branding Guide: Tips to Develop the Best Employer Branding Strategy for 2021 We have penned down this article to cover virtually everything there is to know about employer branding, such as its benefits, how to measure it, how can you improve it, and some coverage on top global companies using market-leading employer branding strategies. To know more about this refer- https://blog.digitalogy.co/employer-branding-strategy/ #best employer branding #best employer branding strategy for 2021 #employer branding #, employer branding 2021 #employer branding and recruitment #employer branding best practices 1641276000 ## DeltaPy⁠⁠ — Tabular Data Augmentation & Feature Engineering ## DeltaPy⁠⁠ — Tabular Data Augmentation & Feature Engineering ## Finance Quant Machine Learning ### Introduction Tabular augmentation is a new experimental space that makes use of novel and traditional data generation and synthesisation techniques to improve model prediction success. It is in essence a process of modular feature engineering and observation engineering while emphasising the order of augmentation to achieve the best predicted outcome from a given information set. DeltaPy was created with finance applications in mind, but it can be broadly applied to any data-rich environment. To take full advantage of tabular augmentation for time-series you would perform the techniques in the following order: (1) transforming, (2) interacting, (3) mapping, (4) extracting, and (5) synthesising. What follows is a practical example of how the above methodology can be used. The purpose here is to establish a framework for table augmentation and to point and guide the user to existing packages. For most the Colab Notebook format might be preferred. I have enabled comments if you want to ask question or address any issues you uncover. For anything pressing use the issues tab. Also have a look at the SSRN report for a more succinct insights. Data augmentation can be defined as any method that could increase the size or improve the quality of a dataset by generating new features or instances without the collection of additional data-points. Data augmentation is of particular importance in image classification tasks where additional data can be created by cropping, padding, or flipping existing images. Tabular cross-sectional and time-series prediction tasks can also benefit from augmentation. Here we divide tabular augmentation into columnular and row-wise methods. Row-wise methods are further divided into extraction and data synthesisation techniques, whereas columnular methods are divided into transformation, interaction, and mapping methods. See the Skeleton Example, for a combination of multiple methods that lead to a halfing of the mean squared error. #### Installation & Citation pip install deltapy  @software{deltapy, title = {{DeltaPy}: Tabular Data Augmentation}, author = {Snow, Derek}, url = {https://github.com/firmai/deltapy/}, version = {0.1.0}, date = {2020-04-11}, }   Snow, Derek, DeltaPy: A Framework for Tabular Data Augmentation in Python (April 22, 2020). Available at SSRN: https://ssrn.com/abstract=3582219  ### Function Glossary Transformation df_out = transform.robust_scaler(df.copy(), drop=["Close_1"]); df_out.head() df_out = transform.standard_scaler(df.copy(), drop=["Close"]); df_out.head() df_out = transform.fast_fracdiff(df.copy(), ["Close","Open"],0.5); df_out.head() df_out = transform.windsorization(df.copy(),"Close",para,strategy='both'); df_out.head() df_out = transform.operations(df.copy(),["Close"]); df_out.head() df_out = transform.triple_exponential_smoothing(df.copy(),["Close"], 12, .2,.2,.2,0); df_out = transform.naive_dec(df.copy(), ["Close","Open"]); df_out.head() df_out = transform.bkb(df.copy(), ["Close"]); df_out.head() df_out = transform.butter_lowpass_filter(df.copy(),["Close"],4); df_out.head() df_out = transform.instantaneous_phases(df.copy(), ["Close"]); df_out.head() df_out = transform.kalman_feat(df.copy(), ["Close"]); df_out.head() df_out = transform.perd_feat(df.copy(),["Close"]); df_out.head() df_out = transform.fft_feat(df.copy(), ["Close"]); df_out.head() df_out = transform.harmonicradar_cw(df.copy(), ["Close"],0.3,0.2); df_out.head() df_out = transform.saw(df.copy(),["Close","Open"]); df_out.head() df_out = transform.modify(df.copy(),["Close"]); df_out.head() df_out = transform.multiple_rolling(df, columns=["Close"]); df_out.head() df_out = transform.multiple_lags(df, start=1, end=3, columns=["Close"]); df_out.head() df_out = transform.prophet_feat(df.copy().reset_index(),["Close","Open"],"Date", "D"); df_out.head()  Interaction df_out = interact.lowess(df.copy(), ["Open","Volume"], df["Close"], f=0.25, iter=3); df_out.head() df_out = interact.autoregression(df.copy()); df_out.head() df_out = interact.muldiv(df.copy(), ["Close","Open"]); df_out.head() df_out = interact.decision_tree_disc(df.copy(), ["Close"]); df_out.head() df_out = interact.quantile_normalize(df.copy(), drop=["Close"]); df_out.head() df_out = interact.tech(df.copy()); df_out.head() df_out = interact.genetic_feat(df.copy()); df_out.head()  Mapping df_out = mapper.pca_feature(df.copy(),variance_or_components=0.80,drop_cols=["Close_1"]); df_out.head() df_out = mapper.cross_lag(df.copy()); df_out.head() df_out = mapper.a_chi(df.copy()); df_out.head() df_out = mapper.encoder_dataset(df.copy(), ["Close_1"], 15); df_out.head() df_out = mapper.lle_feat(df.copy(),["Close_1"],4); df_out.head() df_out = mapper.feature_agg(df.copy(),["Close_1"],4 ); df_out.head() df_out = mapper.neigh_feat(df.copy(),["Close_1"],4 ); df_out.head()  Extraction extract.abs_energy(df["Close"]) extract.cid_ce(df["Close"], True) extract.mean_abs_change(df["Close"]) extract.mean_second_derivative_central(df["Close"]) extract.variance_larger_than_standard_deviation(df["Close"]) extract.var_index(df["Close"].values,var_index_param) extract.symmetry_looking(df["Close"]) extract.has_duplicate_max(df["Close"]) extract.partial_autocorrelation(df["Close"]) extract.augmented_dickey_fuller(df["Close"]) extract.gskew(df["Close"]) extract.stetson_mean(df["Close"]) extract.length(df["Close"]) extract.count_above_mean(df["Close"]) extract.longest_strike_below_mean(df["Close"]) extract.wozniak(df["Close"]) extract.last_location_of_maximum(df["Close"]) extract.fft_coefficient(df["Close"]) extract.ar_coefficient(df["Close"]) extract.index_mass_quantile(df["Close"]) extract.number_cwt_peaks(df["Close"]) extract.spkt_welch_density(df["Close"]) extract.linear_trend_timewise(df["Close"]) extract.c3(df["Close"]) extract.binned_entropy(df["Close"]) extract.svd_entropy(df["Close"].values) extract.hjorth_complexity(df["Close"]) extract.max_langevin_fixed_point(df["Close"]) extract.percent_amplitude(df["Close"]) extract.cad_prob(df["Close"]) extract.zero_crossing_derivative(df["Close"]) extract.detrended_fluctuation_analysis(df["Close"]) extract.fisher_information(df["Close"]) extract.higuchi_fractal_dimension(df["Close"]) extract.petrosian_fractal_dimension(df["Close"]) extract.hurst_exponent(df["Close"]) extract.largest_lyauponov_exponent(df["Close"]) extract.whelch_method(df["Close"]) extract.find_freq(df["Close"]) extract.flux_perc(df["Close"]) extract.range_cum_s(df["Close"]) extract.structure_func(df["Close"]) extract.kurtosis(df["Close"]) extract.stetson_k(df["Close"])  Test sets should ideally not be preprocessed with the training data, as in such a way one could be peaking ahead in the training data. The preprocessing parameters should be identified on the test set and then applied on the test set, i.e., the test set should not have an impact on the transformation applied. As an example, you would learn the parameters of PCA decomposition on the training set and then apply the parameters to both the train and the test set. The benefit of pipelines become clear when one wants to apply multiple augmentation methods. It makes it easy to learn the parameters and then apply them widely. For the most part, this notebook does not concern itself with 'peaking ahead' or pipelines, for some functions, one might have to restructure to code and make use of open source packages to create your preferred solution. ## Documentation by Example Notebook Dependencies pip install deltapy  pip install pykalman pip install tsaug pip install ta pip install tsaug pip install pandasvault pip install gplearn pip install ta pip install seasonal pip install pandasvault  ### Data and Package Load import pandas as pd import numpy as np from deltapy import transform, interact, mapper, extract import warnings warnings.filterwarnings('ignore') def data_copy(): df = pd.read_csv("https://github.com/firmai/random-assets-two/raw/master/numpy/tsla.csv") df["Close_1"] = df["Close"].shift(-1) df = df.dropna() df["Date"] = pd.to_datetime(df["Date"]) df = df.set_index("Date") return df df = data_copy(); df.head()  Some of these categories are fluid and some techniques could fit into multiple buckets. This is an attempt to find an exhaustive number of techniques, but not an exhaustive list of implementations of the techniques. For example, there are thousands of ways to smooth a time-series, but we have only includes 1-2 techniques of interest under each category. ### (1) Transformation: 1. Scaling/Normalisation 2. Standardisation 3. Differencing 4. Capping 5. Operations 6. Smoothing 7. Decomposing 8. Filtering 9. Spectral Analysis 10. Waveforms 11. Modifications 12. Rolling 13. Lagging 14. Forecast Model ### (2) Interaction: 1. Regressions 2. Operators 3. Discretising 4. Normalising 5. Distance 6. Speciality 7. Genetic ### (3) Mapping: 1. Eigen Decomposition 2. Cross Decomposition 3. Kernel Approximation 4. Autoencoder 5. Manifold Learning 6. Clustering 7. Neighbouring ### (4) Extraction: 1. Energy 2. Distance 3. Differencing 4. Derivative 5. Volatility 6. Shape 7. Occurrence 8. Autocorrelation 9. Stochasticity 10. Averages 11. Size 12. Count 13. Streaks 14. Location 15. Model Coefficients 16. Quantile 17. Peaks 18. Density 19. Linearity 20. Non-linearity 21. Entropy 22. Fixed Points 23. Amplitude 24. Probability 25. Crossings 26. Fluctuation 27. Information 28. Fractals 29. Exponent 30. Spectral Analysis 31. Percentile 32. Range 33. Structural 34. Distribution ## (1) Transformation Here transformation is any method that includes only one feature as an input to produce a new feature/s. Transformations can be applied to cross-section and time-series data. Some transformations are exclusive to time-series data (smoothing, filtering), but a handful of functions apply to both. Where the time series methods has a centred mean, or are forward-looking, there is a need to recalculate the outputed time series on a running basis to ensure that information of the future does not leak into the model. The last value of this recalculated series or an extracted feature from this series can then be used as a running value that is only backward looking, satisfying the no 'peaking' ahead rule. There are some packaged in Python that dynamically create time series and extracts their features, but none that incoropates the dynamic creation of a time series in combination with a wide application of prespecified list of extractions. Because this technique is expensive, we have a preference for models that only take historical data into account. In this section we will include a list of all types of transformations, those that only use present information (operations), those that incorporate all values (interpolation methods), those that only include past values (smoothing functions), and those that incorporate a subset window of lagging and leading values (select filters). Only those that use historical values or are turned into prediction methods can be used out of the box. The entire time series can be used in the model development process for historical value methods, and only the forecasted values can be used for prediction models. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data. When using an interpolation method, you are taking future information into account e.g, cubic spline. You can use interpolation methods to forecast into the future (extrapolation), and then use those forecasts in a training set. Or you could recalculate the interpolation for each time step and then extract features out of that series (extraction method). Interpolation and other forward-looking methods can be used if they are turned into prediction problems, then the forecasted values can be trained and tested on, and the fitted data can be diregarded. In the list presented below the first five methods can be used for cross-section and time series data, after that the time-series only methods follow. #### (1) Scaling/Normalisation There are a multitude of scaling methods available. Scaling generally gets applied to the entire dataset and is especially necessary for certain algorithms. K-means make use of euclidean distance hence the need for scaling. For PCA because we are trying to identify the feature with maximus variance we also need scaling. Similarly, we need scaled features for gradient descent. Any algorithm that is not based on a distance measure is not affected by feature scaling. Some of the methods include range scalers like minimum-maximum scaler, maximum absolute scaler or even standardisation methods like the standard scaler can be used for scaling. The example used here is robust scaler. Normalisation is a good technique when you don't know the distribution of the data. Scaling looks into the future, so parameters have to be training on a training set and applied to a test set. (i) Robust Scaler Scaling according to the interquartile range, making it robust to outliers. def robust_scaler(df, drop=None,quantile_range=(25, 75) ): if drop: keep = df[drop] df = df.drop(drop, axis=1) center = np.median(df, axis=0) quantiles = np.percentile(df, quantile_range, axis=0) scale = quantiles[1] - quantiles[0] df = (df - center) / scale if drop: df = pd.concat((keep,df),axis=1) return df df_out = transform.robust_scaler(df.copy(), drop=["Close_1"]); df_out.head()  #### (2) Standardisation When using a standardisation method, it is often more effective when the attribute itself if Gaussian. It is also useful to apply the technique when the model you want to use makes assumptions of Gaussian distributions like linear regression, logistic regression, and linear discriminant analysis. For most applications, standardisation is recommended. (i) Standard Scaler Standardize features by removing the mean and scaling to unit variance def standard_scaler(df,drop ): if drop: keep = df[drop] df = df.drop(drop, axis=1) mean = np.mean(df, axis=0) scale = np.std(df, axis=0) df = (df - mean) / scale if drop: df = pd.concat((keep,df),axis=1) return df df_out = transform.standard_scaler(df.copy(), drop=["Close"]); df_out.head()  #### (3) Differencing Computing the differences between consecutive observation, normally used to obtain a stationary time series. (i) Fractional Differencing Fractional differencing, allows us to achieve stationarity while maintaining the maximum amount of memory compared to integer differencing. import pylab as pl def fast_fracdiff(x, cols, d): for col in cols: T = len(x[col]) np2 = int(2 ** np.ceil(np.log2(2 * T - 1))) k = np.arange(1, T) b = (1,) + tuple(np.cumprod((k - d - 1) / k)) z = (0,) * (np2 - T) z1 = b + z z2 = tuple(x[col]) + z dx = pl.ifft(pl.fft(z1) * pl.fft(z2)) x[col+"_frac"] = np.real(dx[0:T]) return x df_out = transform.fast_fracdiff(df.copy(), ["Close","Open"],0.5); df_out.head()  #### (4) Capping Any method that provides sets a floor and a cap to a feature's value. Capping can affect the distribution of data, so it should not be exagerated. One can cap values by using the average, by using the max and min values, or by an arbitrary extreme value. (i) Winzorisation The transformation of features by limiting extreme values in the statistical data to reduce the effect of possibly spurious outliers by replacing it with a certain percentile value. def outlier_detect(data,col,threshold=1,method="IQR"): if method == "IQR": IQR = data[col].quantile(0.75) - data[col].quantile(0.25) Lower_fence = data[col].quantile(0.25) - (IQR * threshold) Upper_fence = data[col].quantile(0.75) + (IQR * threshold) if method == "STD": Upper_fence = data[col].mean() + threshold * data[col].std() Lower_fence = data[col].mean() - threshold * data[col].std() if method == "OWN": Upper_fence = data[col].mean() + threshold * data[col].std() Lower_fence = data[col].mean() - threshold * data[col].std() if method =="MAD": median = data[col].median() median_absolute_deviation = np.median([np.abs(y - median) for y in data[col]]) modified_z_scores = pd.Series([0.6745 * (y - median) / median_absolute_deviation for y in data[col]]) outlier_index = np.abs(modified_z_scores) > threshold print('Num of outlier detected:',outlier_index.value_counts()[1]) print('Proportion of outlier detected',outlier_index.value_counts()[1]/len(outlier_index)) return outlier_index, (median_absolute_deviation, median_absolute_deviation) para = (Upper_fence, Lower_fence) tmp = pd.concat([data[col]>Upper_fence,data[col]<Lower_fence],axis=1) outlier_index = tmp.any(axis=1) print('Num of outlier detected:',outlier_index.value_counts()[1]) print('Proportion of outlier detected',outlier_index.value_counts()[1]/len(outlier_index)) return outlier_index, para def windsorization(data,col,para,strategy='both'): """ top-coding & bottom coding (capping the maximum of a distribution at an arbitrarily set value,vice versa) """ data_copy = data.copy(deep=True) if strategy == 'both': data_copy.loc[data_copy[col]>para[0],col] = para[0] data_copy.loc[data_copy[col]<para[1],col] = para[1] elif strategy == 'top': data_copy.loc[data_copy[col]>para[0],col] = para[0] elif strategy == 'bottom': data_copy.loc[data_copy[col]<para[1],col] = para[1] return data_copy _, para = transform.outlier_detect(df, "Close") df_out = transform.windsorization(df.copy(),"Close",para,strategy='both'); df_out.head()  #### (5) Operations Operations here are treated like traditional transformations. It is the replacement of a variable by a function of that variable. In a stronger sense, a transformation is a replacement that changes the shape of a distribution or relationship. (i) Power, Log, Recipricol, Square Root def operations(df,features): df_new = df[features] df_new = df_new - df_new.min() sqr_name = [str(fa)+"_POWER_2" for fa in df_new.columns] log_p_name = [str(fa)+"_LOG_p_one_abs" for fa in df_new.columns] rec_p_name = [str(fa)+"_RECIP_p_one" for fa in df_new.columns] sqrt_name = [str(fa)+"_SQRT_p_one" for fa in df_new.columns] df_sqr = pd.DataFrame(np.power(df_new.values, 2),columns=sqr_name, index=df.index) df_log = pd.DataFrame(np.log(df_new.add(1).abs().values),columns=log_p_name, index=df.index) df_rec = pd.DataFrame(np.reciprocal(df_new.add(1).values),columns=rec_p_name, index=df.index) df_sqrt = pd.DataFrame(np.sqrt(df_new.abs().add(1).values),columns=sqrt_name, index=df.index) dfs = [df, df_sqr, df_log, df_rec, df_sqrt] df= pd.concat(dfs, axis=1) return df df_out = transform.operations(df.copy(),["Close"]); df_out.head()  #### (6) Smoothing Here we maintain that any method that has a component of historical averaging is a smoothing method such as a simple moving average and single, double and tripple exponential smoothing methods. These forms of non-causal filters are also popular in signal processing and are called filters, where exponential smoothing is called an IIR filter and a moving average a FIR filter with equal weighting factors. (i) Tripple Exponential Smoothing (Holt-Winters Exponential Smoothing) The Holt-Winters seasonal method comprises the forecast equation and three smoothing equations — one for the level$ℓt$, one for the trend &bt&, and one for the seasonal component$st$. This particular version is performed by looking at the last 12 periods. For that reason, the first 12 records should be disregarded because they can't make use of the required window size for a fair calculation. The calculation is such that values are still provided for those periods based on whatever data might be available. def initial_trend(series, slen): sum = 0.0 for i in range(slen): sum += float(series[i+slen] - series[i]) / slen return sum / slen def initial_seasonal_components(series, slen): seasonals = {} season_averages = [] n_seasons = int(len(series)/slen) # compute season averages for j in range(n_seasons): season_averages.append(sum(series[slen*j:slen*j+slen])/float(slen)) # compute initial values for i in range(slen): sum_of_vals_over_avg = 0.0 for j in range(n_seasons): sum_of_vals_over_avg += series[slen*j+i]-season_averages[j] seasonals[i] = sum_of_vals_over_avg/n_seasons return seasonals def triple_exponential_smoothing(df,cols, slen, alpha, beta, gamma, n_preds): for col in cols: result = [] seasonals = initial_seasonal_components(df[col], slen) for i in range(len(df[col])+n_preds): if i == 0: # initial values smooth = df[col][0] trend = initial_trend(df[col], slen) result.append(df[col][0]) continue if i >= len(df[col]): # we are forecasting m = i - len(df[col]) + 1 result.append((smooth + m*trend) + seasonals[i%slen]) else: val = df[col][i] last_smooth, smooth = smooth, alpha*(val-seasonals[i%slen]) + (1-alpha)*(smooth+trend) trend = beta * (smooth-last_smooth) + (1-beta)*trend seasonals[i%slen] = gamma*(val-smooth) + (1-gamma)*seasonals[i%slen] result.append(smooth+trend+seasonals[i%slen]) df[col+"_TES"] = result #print(seasonals) return df df_out= transform.triple_exponential_smoothing(df.copy(),["Close"], 12, .2,.2,.2,0); df_out.head()  #### (7) Decomposing Decomposition procedures are used in time series to describe the trend and seasonal factors in a time series. More extensive decompositions might also include long-run cycles, holiday effects, day of week effects and so on. Here, we’ll only consider trend and seasonal decompositions. A naive decomposition makes use of moving averages, other decomposition methods are available that make use of LOESS. (i) Naive Decomposition The base trend takes historical information into account and established moving averages; it does not have to be linear. To estimate the seasonal component for each season, simply average the detrended values for that season. If the seasonal variation looks constant, we should use the additive model. If the magnitude is increasing as a function of time, we will use multiplicative. Here because it is predictive in nature we are using a one sided moving average, as opposed to a two-sided centred average. import statsmodels.api as sm def naive_dec(df, columns, freq=2): for col in columns: decomposition = sm.tsa.seasonal_decompose(df[col], model='additive', freq = freq, two_sided=False) df[col+"_NDDT" ] = decomposition.trend df[col+"_NDDT"] = decomposition.seasonal df[col+"_NDDT"] = decomposition.resid return df df_out = transform.naive_dec(df.copy(), ["Close","Open"]); df_out.head()  #### (8) Filtering It is often useful to either low-pass filter (smooth) time series in order to reveal low-frequency features and trends, or to high-pass filter (detrend) time series in order to isolate high frequency transients (e.g. storms). Low pass filters use historical values, high-pass filters detrends with low-pass filters, so also indirectly uses historical values. There are a few filters available, closely associated with decompositions and smoothing functions. The Hodrick-Prescott filter separates a time-series$yt$into a trend$τt$and a cyclical component$ζt$. The Christiano-Fitzgerald filter is a generalization of Baxter-King filter and can be seen as weighted moving average. (i) Baxter-King Bandpass The Baxter-King filter is intended to explicitly deal with the periodicity of the business cycle. By applying their band-pass filter to a series, they produce a new series that does not contain fluctuations at higher or lower than those of the business cycle. The parameters are arbitrarily chosen. This method uses a centred moving average that has to be changed to a lagged moving average before it can be used as an input feature. The maximum period of oscillation should be used as the point to truncate the dataset, as that part of the time series does not incorporate all the required datapoints. import statsmodels.api as sm def bkb(df, cols): for col in cols: df[col+"_BPF"] = sm.tsa.filters.bkfilter(df[[col]].values, 2, 10, len(df)-1) return df df_out = transform.bkb(df.copy(), ["Close"]); df_out.head()  (ii) Butter Lowpass (IIR Filter Design) The Butterworth filter is a type of signal processing filter designed to have a frequency response as flat as possible in the passban. Like other filtersm the first few values have to be disregarded for accurate downstream prediction. Instead of disregarding these values on a per case basis, they can be diregarded in one chunk once the database of transformed features have been developed. from scipy import signal, integrate def butter_lowpass(cutoff, fs=20, order=5): nyq = 0.5 * fs normal_cutoff = cutoff / nyq b, a = signal.butter(order, normal_cutoff, btype='low', analog=False) return b, a def butter_lowpass_filter(df,cols, cutoff, fs=20, order=5): b, a = butter_lowpass(cutoff, fs, order=order) for col in cols: df[col+"_BUTTER"] = signal.lfilter(b, a, df[col]) return df df_out = transform.butter_lowpass_filter(df.copy(),["Close"],4); df_out.head()  (iii) Hilbert Transform Angle The Hilbert transform is a time-domain to time-domain transformation which shifts the phase of a signal by 90 degrees. It is also a centred measure and would be difficult to use in a time series prediction setting, unless it is recalculated on a per step basis or transformed to be based on historical values only. from scipy import signal import numpy as np def instantaneous_phases(df,cols): for col in cols: df[col+"_HILLB"] = np.unwrap(np.angle(signal.hilbert(df[col], axis=0)), axis=0) return df df_out = transform.instantaneous_phases(df.copy(), ["Close"]); df_out.head()  (iiiv) Unscented Kalman Filter The Kalman filter is better suited for estimating things that change over time. The most tangible example is tracking moving objects. A Kalman filter will be very close to the actual trajectory because it says the most recent measurement is more important than the older ones. The Unscented Kalman Filter (UKF) is a model based-techniques that recursively estimates the states (and with some modifications also parameters) of a nonlinear, dynamic, discrete-time system. The UKF is based on the typical prediction-correction style methods. The Kalman Smoother incorporates future values, the Filter doesn't and can be used for online prediction. The normal Kalman filter is a forward filter in the sense that it makes forecast of the current state using only current and past observations, whereas the smoother is based on computing a suitable linear combination of two filters, which are ran in forward and backward directions. from pykalman import UnscentedKalmanFilter def kalman_feat(df, cols): for col in cols: ukf = UnscentedKalmanFilter(lambda x, w: x + np.sin(w), lambda x, v: x + v, observation_covariance=0.1) (filtered_state_means, filtered_state_covariances) = ukf.filter(df[col]) (smoothed_state_means, smoothed_state_covariances) = ukf.smooth(df[col]) df[col+"_UKFSMOOTH"] = smoothed_state_means.flatten() df[col+"_UKFFILTER"] = filtered_state_means.flatten() return df df_out = transform.kalman_feat(df.copy(), ["Close"]); df_out.head()  #### (9) Spectral Analysis There are a range of functions for spectral analysis. You can use periodograms and the welch method to estimate the power spectral density. You can also use the welch method to estimate the cross power spectral density. Other techniques include spectograms, Lomb-Scargle periodograms and, short time fourier transform. (i) Periodogram This returns an array of sample frequencies and the power spectrum of x, or the power spectral density of x. from scipy import signal def perd_feat(df, cols): for col in cols: sig = signal.periodogram(df[col],fs=1, return_onesided=False) df[col+"_FREQ"] = sig[0] df[col+"_POWER"] = sig[1] return df df_out = transform.perd_feat(df.copy(),["Close"]); df_out.head()  (ii) Fast Fourier Transform The FFT, or fast fourier transform is an algorithm that essentially uses convolution techniques to efficiently find the magnitude and location of the tones that make up the signal of interest. We can often play with the FFT spectrum, by adding and removing successive tones (which is akin to selectively filtering particular tones that make up the signal), in order to obtain a smoothed version of the underlying signal. This takes the entire signal into account, and as a result has to be recalculated on a running basis to avoid peaking into the future. def fft_feat(df, cols): for col in cols: fft_df = np.fft.fft(np.asarray(df[col].tolist())) fft_df = pd.DataFrame({'fft':fft_df}) df[col+'_FFTABS'] = fft_df['fft'].apply(lambda x: np.abs(x)).values df[col+'_FFTANGLE'] = fft_df['fft'].apply(lambda x: np.angle(x)).values return df df_out = transform.fft_feat(df.copy(), ["Close"]); df_out.head()  #### (10) Waveforms The waveform of a signal is the shape of its graph as a function of time. (i) Continuous Wave Radar from scipy import signal def harmonicradar_cw(df, cols, fs,fc): for col in cols: ttxt = f'CW: {fc} Hz' #%% input t = df[col] tx = np.sin(2*np.pi*fc*t) _,Pxx = signal.welch(tx,fs) #%% diode d = (signal.square(2*np.pi*fc*t)) d[d<0] = 0. #%% output of diode rx = tx * d df[col+"_HARRAD"] = rx.values return df df_out = transform.harmonicradar_cw(df.copy(), ["Close"],0.3,0.2); df_out.head()  (ii) Saw Tooth Return a periodic sawtooth or triangle waveform. def saw(df, cols): for col in cols: df[col+" SAW"] = signal.sawtooth(df[col]) return df df_out = transform.saw(df.copy(),["Close","Open"]); df_out.head()  (9) Modifications A range of modification usually applied ot images, these values would have to be recalculate for each time-series. (i) Various Techniques from tsaug import * def modify(df, cols): for col in cols: series = df[col].values df[col+"_magnify"], _ = magnify(series, series) df[col+"_affine"], _ = affine(series, series) df[col+"_crop"], _ = crop(series, series) df[col+"_cross_sum"], _ = cross_sum(series, series) df[col+"_resample"], _ = resample(series, series) df[col+"_trend"], _ = trend(series, series) df[col+"_random_affine"], _ = random_time_warp(series, series) df[col+"_random_crop"], _ = random_crop(series, series) df[col+"_random_cross_sum"], _ = random_cross_sum(series, series) df[col+"_random_sidetrack"], _ = random_sidetrack(series, series) df[col+"_random_time_warp"], _ = random_time_warp(series, series) df[col+"_random_magnify"], _ = random_magnify(series, series) df[col+"_random_jitter"], _ = random_jitter(series, series) df[col+"_random_trend"], _ = random_trend(series, series) return df df_out = transform.modify(df.copy(),["Close"]); df_out.head()  #### (11) Rolling Features that are calculated on a rolling basis over fixed window size. (i) Mean, Standard Deviation def multiple_rolling(df, windows = [1,2], functions=["mean","std"], columns=None): windows = [1+a for a in windows] if not columns: columns = df.columns.to_list() rolling_dfs = (df[columns].rolling(i) # 1. Create window .agg(functions) # 1. Aggregate .rename({col: '{0}_{1:d}'.format(col, i) for col in columns}, axis=1) # 2. Rename columns for i in windows) # For each window df_out = pd.concat((df, *rolling_dfs), axis=1) da = df_out.iloc[:,len(df.columns):] da = [col[0] + "_" + col[1] for col in da.columns.to_list()] df_out.columns = df.columns.to_list() + da return df_out # 3. Concatenate dataframes df_out = transform.multiple_rolling(df, columns=["Close"]); df_out.head()  #### (12) Lagging Lagged values from existing features. (i) Single Steps def multiple_lags(df, start=1, end=3,columns=None): if not columns: columns = df.columns.to_list() lags = range(start, end+1) # Just two lags for demonstration. df = df.assign(**{ '{}_t_{}'.format(col, t): df[col].shift(t) for t in lags for col in columns }) return df df_out = transform.multiple_lags(df, start=1, end=3, columns=["Close"]); df_out.head()  #### (13) Forecast Model There are a range of time series model that can be implemented like AR, MA, ARMA, ARIMA, SARIMA, SARIMAX, VAR, VARMA, VARMAX, SES, and HWES. The models can be divided into autoregressive models and smoothing models. In an autoregression model, we forecast the variable of interest using a linear combination of past values of the variable. Each method might requre specific tuning and parameters to suit your prediction task. You need to drop a certain amount of historical data that you use during the fitting stage. Models that take seasonality into account need more training data. (i) Prophet Prophet is a procedure for forecasting time series data based on an additive model where non-linear trends are fit with yearly, weekly, and daily seasonality. You can apply additive models to your training data but also interactive models like deep learning models. The problem is that because these models have learned from future observations, there would this be a need to recalculate the time series on a running basis, or to only include the predicted as opposed to fitted values in future training and test sets. In this example, I train on 150 data points to illustrate how the remaining or so 100 datapoints can be used in a new prediction problem. You can plot with df["PROPHET"].plot() to see the effect. You can apply additive models to your training data but also interactive models like deep learning models. The problem is that these models have learned from future observations, there would this be a need to recalculate the time series on a running basis, or to only include the predicted as opposed to fitted values in future training and test sets. from fbprophet import Prophet def prophet_feat(df, cols,date, freq,train_size=150): def prophet_dataframe(df): df.columns = ['ds','y'] return df def original_dataframe(df, freq, name): prophet_pred = pd.DataFrame({"Date" : df['ds'], name : df["yhat"]}) prophet_pred = prophet_pred.set_index("Date") #prophet_pred.index.freq = pd.tseries.frequencies.to_offset(freq) return prophet_pred[name].values for col in cols: model = Prophet(daily_seasonality=True) fb = model.fit(prophet_dataframe(df[[date, col]].head(train_size))) forecast_len = len(df) - train_size future = model.make_future_dataframe(periods=forecast_len,freq=freq) future_pred = model.predict(future) df[col+"_PROPHET"] = list(original_dataframe(future_pred,freq,col)) return df df_out = transform.prophet_feat(df.copy().reset_index(),["Close","Open"],"Date", "D"); df_out.head()  ## (2) Interaction Interactions are defined as methods that require more than one feature to create an additional feature. Here we include normalising and discretising techniques that are non-feature specific. Almost all of these method can be applied to cross-section method. The only methods that are time specific is the technical features in the speciality section and the autoregression model. #### (1) Regression Regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome variable') and one or more independent variables. (i) Lowess Smoother The lowess smoother is a robust locally weighted regression. The function fits a nonparametric regression curve to a scatterplot. from math import ceil import numpy as np from scipy import linalg import math def lowess(df, cols, y, f=2. / 3., iter=3): for col in cols: n = len(df[col]) r = int(ceil(f * n)) h = [np.sort(np.abs(df[col] - df[col][i]))[r] for i in range(n)] w = np.clip(np.abs((df[col][:, None] - df[col][None, :]) / h), 0.0, 1.0) w = (1 - w ** 3) ** 3 yest = np.zeros(n) delta = np.ones(n) for iteration in range(iter): for i in range(n): weights = delta * w[:, i] b = np.array([np.sum(weights * y), np.sum(weights * y * df[col])]) A = np.array([[np.sum(weights), np.sum(weights * df[col])], [np.sum(weights * df[col]), np.sum(weights * df[col] * df[col])]]) beta = linalg.solve(A, b) yest[i] = beta[0] + beta[1] * df[col][i] residuals = y - yest s = np.median(np.abs(residuals)) delta = np.clip(residuals / (6.0 * s), -1, 1) delta = (1 - delta ** 2) ** 2 df[col+"_LOWESS"] = yest return df df_out = interact.lowess(df.copy(), ["Open","Volume"], df["Close"], f=0.25, iter=3); df_out.head()  Autoregression Autoregression is a time series model that uses observations from previous time steps as input to a regression equation to predict the value at the next time step from statsmodels.tsa.ar_model import AR from timeit import default_timer as timer def autoregression(df, drop=None, settings={"autoreg_lag":4}): autoreg_lag = settings["autoreg_lag"] if drop: keep = df[drop] df = df.drop([drop],axis=1).values n_channels = df.shape[0] t = timer() channels_regg = np.zeros((n_channels, autoreg_lag + 1)) for i in range(0, n_channels): fitted_model = AR(df.values[i, :]).fit(autoreg_lag) # TODO: This is not the same as Matlab's for some reasons! # kk = ARMAResults(fitted_model) # autore_vals, dummy1, dummy2 = arburg(x[i, :], autoreg_lag) # This looks like Matlab's but slow channels_regg[i, 0: len(fitted_model.params)] = np.real(fitted_model.params) for i in range(channels_regg.shape[1]): df["LAG_"+str(i+1)] = channels_regg[:,i] if drop: df = pd.concat((keep,df),axis=1) t = timer() - t return df df_out = interact.autoregression(df.copy()); df_out.head()  #### (2) Operator Looking at interaction between different features. Here the methods employed are multiplication and division. (i) Multiplication and Division def muldiv(df, feature_list): for feat in feature_list: for feat_two in feature_list: if feat==feat_two: continue else: df[feat+"/"+feat_two] = df[feat]/(df[feat_two]-df[feat_two].min()) #zero division guard df[feat+"_X_"+feat_two] = df[feat]*(df[feat_two]) return df df_out = interact.muldiv(df.copy(), ["Close","Open"]); df_out.head()  #### (3) Discretising In statistics and machine learning, discretization refers to the process of converting or partitioning continuous attributes, features or variables to discretized or nominal attributes (i) Decision Tree Discretiser The first method that will be applies here is a supersived discretiser. Discretisation with Decision Trees consists of using a decision tree to identify the optimal splitting points that would determine the bins or contiguous intervals. from sklearn.tree import DecisionTreeRegressor def decision_tree_disc(df, cols, depth=4 ): for col in cols: df[col +"_m1"] = df[col].shift(1) df = df.iloc[1:,:] tree_model = DecisionTreeRegressor(max_depth=depth,random_state=0) tree_model.fit(df[col +"_m1"].to_frame(), df[col]) df[col+"_Disc"] = tree_model.predict(df[col +"_m1"].to_frame()) return df df_out = interact.decision_tree_disc(df.copy(), ["Close"]); df_out.head()  #### (4) Normalising Normalising normally pertains to the scaling of data. There are many method available, interacting normalising methods makes use of all the feature's attributes to do the scaling. (i) Quantile Normalisation In statistics, quantile normalization is a technique for making two distributions identical in statistical properties. import numpy as np import pandas as pd def quantile_normalize(df, drop): if drop: keep = df[drop] df = df.drop(drop,axis=1) #compute rank dic = {} for col in df: dic.update({col : sorted(df[col])}) sorted_df = pd.DataFrame(dic) rank = sorted_df.mean(axis = 1).tolist() #sort for col in df: t = np.searchsorted(np.sort(df[col]), df[col]) df[col] = [rank[i] for i in t] if drop: df = pd.concat((keep,df),axis=1) return df df_out = interact.quantile_normalize(df.copy(), drop=["Close"]); df_out.head()  #### (5) Distance There are multiple types of distance functions like Euclidean, Mahalanobis, and Minkowski distance. Here we are using a contrived example in a location based haversine distance. (i) Haversine Distance The Haversine (or great circle) distance is the angular distance between two points on the surface of a sphere. from math import sin, cos, sqrt, atan2, radians def haversine_distance(row, lon="Open", lat="Close"): c_lat,c_long = radians(52.5200), radians(13.4050) R = 6373.0 long = radians(row['Open']) lat = radians(row['Close']) dlon = long - c_long dlat = lat - c_lat a = sin(dlat / 2)**2 + cos(lat) * cos(c_lat) * sin(dlon / 2)**2 c = 2 * atan2(sqrt(a), sqrt(1 - a)) return R * c df_out['distance_central'] = df.apply(interact.haversine_distance,axis=1); df_out.head()  #### (6) Speciality (i) Technical Features Technical indicators are heuristic or mathematical calculations based on the price, volume, or open interest of a security or contract used by traders who follow technical analysis. By analyzing historical data, technical analysts use indicators to predict future price movements. import ta def tech(df): return ta.add_all_ta_features(df, open="Open", high="High", low="Low", close="Close", volume="Volume") df_out = interact.tech(df.copy()); df_out.head()  #### (7) Genetic Genetic programming has shown promise in constructing feature by osing original features to form high-level ones that can help algorithms achieve better performance. (i) Symbolic Transformer A symbolic transformer is a supervised transformer that begins by building a population of naive random formulas to represent a relationship. df.head()  from gplearn.genetic import SymbolicTransformer def genetic_feat(df, num_gen=20, num_comp=10): function_set = ['add', 'sub', 'mul', 'div', 'sqrt', 'log', 'abs', 'neg', 'inv','tan'] gp = SymbolicTransformer(generations=num_gen, population_size=200, hall_of_fame=100, n_components=num_comp, function_set=function_set, parsimony_coefficient=0.0005, max_samples=0.9, verbose=1, random_state=0, n_jobs=6) gen_feats = gp.fit_transform(df.drop("Close_1", axis=1), df["Close_1"]); df.iloc[:,:8] gen_feats = pd.DataFrame(gen_feats, columns=["gen_"+str(a) for a in range(gen_feats.shape[1])]) gen_feats.index = df.index return pd.concat((df,gen_feats),axis=1) df_out = interact.genetic_feat(df.copy()); df_out.head()  ## (3) Mapping Methods that help with the summarisation of features by remapping them to achieve some aim like the maximisation of variability or class separability. These methods tend to be unsupervised, but can also take an supervised form. #### (1) Eigen Decomposition Eigendecomposition or sometimes spectral decomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors. Some examples are LDA and PCA. (i) Principal Component Analysis Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. def pca_feature(df, memory_issues=False,mem_iss_component=False,variance_or_components=0.80,n_components=5 ,drop_cols=None, non_linear=True): if non_linear: pca = KernelPCA(n_components = n_components, kernel='rbf', fit_inverse_transform=True, random_state = 33, remove_zero_eig= True) else: if memory_issues: if not mem_iss_component: raise ValueError("If you have memory issues, you have to preselect mem_iss_component") pca = IncrementalPCA(mem_iss_component) else: if variance_or_components>1: pca = PCA(n_components=variance_or_components) else: # automated selection based on variance pca = PCA(n_components=variance_or_components,svd_solver="full") if drop_cols: X_pca = pca.fit_transform(df.drop(drop_cols,axis=1)) return pd.concat((df[drop_cols],pd.DataFrame(X_pca, columns=["PCA_"+str(i+1) for i in range(X_pca.shape[1])],index=df.index)),axis=1) else: X_pca = pca.fit_transform(df) return pd.DataFrame(X_pca, columns=["PCA_"+str(i+1) for i in range(X_pca.shape[1])],index=df.index) return df df_out = mapper.pca_feature(df.copy(), variance_or_components=0.9, n_components=8,non_linear=False)  #### (2) Cross Decomposition These families of algorithms are useful to find linear relations between two multivariate datasets. (1) Canonical Correlation Analysis Canonical-correlation analysis (CCA) is a way of inferring information from cross-covariance matrices. from sklearn.cross_decomposition import CCA def cross_lag(df, drop=None, lags=1, components=4 ): if drop: keep = df[drop] df = df.drop([drop],axis=1) df_2 = df.shift(lags) df = df.iloc[lags:,:] df_2 = df_2.dropna().reset_index(drop=True) cca = CCA(n_components=components) cca.fit(df_2, df) X_c, df_2 = cca.transform(df_2, df) df_2 = pd.DataFrame(df_2, index=df.index) df_2 = df.add_prefix('crd_') if drop: df = pd.concat([keep,df,df_2],axis=1) else: df = pd.concat([df,df_2],axis=1) return df df_out = mapper.cross_lag(df.copy()); df_out.head()  #### (3) Kernel Approximation Functions that approximate the feature mappings that correspond to certain kernels, as they are used for example in support vector machines. (i) Additive Chi2 Kernel Computes the additive chi-squared kernel between observations in X and Y The chi-squared kernel is computed between each pair of rows in X and Y. X and Y have to be non-negative. from sklearn.kernel_approximation import AdditiveChi2Sampler def a_chi(df, drop=None, lags=1, sample_steps=2 ): if drop: keep = df[drop] df = df.drop([drop],axis=1) df_2 = df.shift(lags) df = df.iloc[lags:,:] df_2 = df_2.dropna().reset_index(drop=True) chi2sampler = AdditiveChi2Sampler(sample_steps=sample_steps) df_2 = chi2sampler.fit_transform(df_2, df["Close"]) df_2 = pd.DataFrame(df_2, index=df.index) df_2 = df.add_prefix('achi_') if drop: df = pd.concat([keep,df,df_2],axis=1) else: df = pd.concat([df,df_2],axis=1) return df df_out = mapper.a_chi(df.copy()); df_out.head()  #### (4) Autoencoder An autoencoder is a type of artificial neural network used to learn efficient data codings in an unsupervised manner. The aim of an autoencoder is to learn a representation (encoding) for a set of data, typically for dimensionality reduction, by training the network to ignore noise. (i) Feed Forward The simplest form of an autoencoder is a feedforward, non-recurrent neural network similar to single layer perceptrons that participate in multilayer perceptrons from sklearn.preprocessing import minmax_scale import tensorflow as tf import numpy as np def encoder_dataset(df, drop=None, dimesions=20): if drop: train_scaled = minmax_scale(df.drop(drop,axis=1).values, axis = 0) else: train_scaled = minmax_scale(df.values, axis = 0) # define the number of encoding dimensions encoding_dim = dimesions # define the number of features ncol = train_scaled.shape[1] input_dim = tf.keras.Input(shape = (ncol, )) # Encoder Layers encoded1 = tf.keras.layers.Dense(3000, activation = 'relu')(input_dim) encoded2 = tf.keras.layers.Dense(2750, activation = 'relu')(encoded1) encoded3 = tf.keras.layers.Dense(2500, activation = 'relu')(encoded2) encoded4 = tf.keras.layers.Dense(750, activation = 'relu')(encoded3) encoded5 = tf.keras.layers.Dense(500, activation = 'relu')(encoded4) encoded6 = tf.keras.layers.Dense(250, activation = 'relu')(encoded5) encoded7 = tf.keras.layers.Dense(encoding_dim, activation = 'relu')(encoded6) encoder = tf.keras.Model(inputs = input_dim, outputs = encoded7) encoded_input = tf.keras.Input(shape = (encoding_dim, )) encoded_train = pd.DataFrame(encoder.predict(train_scaled),index=df.index) encoded_train = encoded_train.add_prefix('encoded_') if drop: encoded_train = pd.concat((df[drop],encoded_train),axis=1) return encoded_train df_out = mapper.encoder_dataset(df.copy(), ["Close_1"], 15); df_out.head()  df_out.head()  #### (5) Manifold Learning Manifold Learning can be thought of as an attempt to generalize linear frameworks like PCA to be sensitive to non-linear structure in data. (i) Local Linear Embedding Locally Linear Embedding is a method of non-linear dimensionality reduction. It tries to reduce these n-Dimensions while trying to preserve the geometric features of the original non-linear feature structure. from sklearn.manifold import LocallyLinearEmbedding def lle_feat(df, drop=None, components=4): if drop: keep = df[drop] df = df.drop(drop, axis=1) embedding = LocallyLinearEmbedding(n_components=components) em = embedding.fit_transform(df) df = pd.DataFrame(em,index=df.index) df = df.add_prefix('lle_') if drop: df = pd.concat((keep,df),axis=1) return df df_out = mapper.lle_feat(df.copy(),["Close_1"],4); df_out.head()  #### (6) Clustering Most clustering techniques start with a bottom up approach: each observation starts in its own cluster, and clusters are successively merged together with some measure. Although these clustering techniques are typically used for observations, it can also be used for feature dimensionality reduction; especially hierarchical clustering techniques. (i) Feature Agglomeration Feature agglomerative uses clustering to group together features that look very similar, thus decreasing the number of features. import numpy as np from sklearn import datasets, cluster def feature_agg(df, drop=None, components=4): if drop: keep = df[drop] df = df.drop(drop, axis=1) components = min(df.shape[1]-1,components) agglo = cluster.FeatureAgglomeration(n_clusters=components) agglo.fit(df) df = pd.DataFrame(agglo.transform(df),index=df.index) df = df.add_prefix('feagg_') if drop: return pd.concat((keep,df),axis=1) else: return df df_out = mapper.feature_agg(df.copy(),["Close_1"],4 ); df_out.head()  #### (7) Neigbouring Neighbouring points can be calculated using distance metrics like Hamming, Manhattan, Minkowski distance. The principle behind nearest neighbor methods is to find a predefined number of training samples closest in distance to the new point, and predict the label from these. (i) Nearest Neighbours Unsupervised learner for implementing neighbor searches. from sklearn.neighbors import NearestNeighbors def neigh_feat(df, drop, neighbors=6): if drop: keep = df[drop] df = df.drop(drop, axis=1) components = min(df.shape[0]-1,neighbors) neigh = NearestNeighbors(n_neighbors=neighbors) neigh.fit(df) neigh = neigh.kneighbors()[0] df = pd.DataFrame(neigh, index=df.index) df = df.add_prefix('neigh_') if drop: return pd.concat((keep,df),axis=1) else: return df return df df_out = mapper.neigh_feat(df.copy(),["Close_1"],4 ); df_out.head()  ## (4) Extraction When working with extraction, you have decide the size of the time series history to take into account when calculating a collection of walk-forward feature values. To facilitate our extraction, we use an excellent package called TSfresh, and also some of their default features. For completeness, we also include 12 or so custom features to be added to the extraction pipeline. The time series methods in the transformation section and the interaction section are similar to the methods we will uncover in the extraction section, however, for transformation and interaction methods the output is an entire new time series, whereas extraction methods takes as input multiple constructed time series and extracts a singular value from each time series to reconstruct an entirely new time series. Some methods naturally fit better in one format over another, e.g., lags are too expensive for extraction; time series decomposition only has to be performed once, because it has a low level of 'leakage' so is better suited to transformation; and forecast methods attempt to predict multiple future training samples, so won't work with extraction that only delivers one value per time series. Furthermore all non time-series (cross-sectional) transformation and extraction techniques can not make use of extraction as it is solely a time-series method. Lastly, when we want to double apply specific functions we can apply it as a transformation/interaction then all the extraction methods can be applied to this feature as well. For example, if we calculate a smoothing function (transformation) then all other extraction functions (median, entropy, linearity etc.) can now be applied to that smoothing function, including the application of the smoothing function itself, e.g., a double smooth, double lag, double filter etc. So separating these methods out give us great flexibility. Decorator def set_property(key, value): """ This method returns a decorator that sets the property key of the function to value """ def decorate_func(func): setattr(func, key, value) if func.__doc__ and key == "fctype": func.__doc__ = func.__doc__ + "\n\n *This function is of type: " + value + "*\n" return func return decorate_func  #### (1) Energy You can calculate the linear, non-linear and absolute energy of a time series. In signal processing, the energy$E_S$of a continuous-time signal$x(t)$is defined as the area under the squared magnitude of the considered signal. Mathematically,$E_{s}=\langle x(t), x(t)\rangle=\int_{-\infty}^{\infty}|x(t)|^{2} d t$(i) Absolute Energy Returns the absolute energy of the time series which is the sum over the squared values #-> In Package def abs_energy(x): if not isinstance(x, (np.ndarray, pd.Series)): x = np.asarray(x) return np.dot(x, x) extract.abs_energy(df["Close"])  #### (2) Distance Here we widely define distance measures as those that take a difference between attributes or series of datapoints. (i) Complexity-Invariant Distance This function calculator is an estimate for a time series complexity. #-> In Package def cid_ce(x, normalize): if not isinstance(x, (np.ndarray, pd.Series)): x = np.asarray(x) if normalize: s = np.std(x) if s!=0: x = (x - np.mean(x))/s else: return 0.0 x = np.diff(x) return np.sqrt(np.dot(x, x)) extract.cid_ce(df["Close"], True)  #### (3) Differencing Many alternatives to differencing exists, one can for example take the difference of every other value, take the squared difference, take the fractional difference, or like our example, take the mean absolute difference. (i) Mean Absolute Change Returns the mean over the absolute differences between subsequent time series values. #-> In Package def mean_abs_change(x): return np.mean(np.abs(np.diff(x))) extract.mean_abs_change(df["Close"])  #### (4) Derivative Features where the emphasis is on the rate of change. (i) Mean Central Second Derivative Returns the mean value of a central approximation of the second derivative #-> In Package def _roll(a, shift): if not isinstance(a, np.ndarray): a = np.asarray(a) idx = shift % len(a) return np.concatenate([a[-idx:], a[:-idx]]) def mean_second_derivative_central(x): diff = (_roll(x, 1) - 2 * np.array(x) + _roll(x, -1)) / 2.0 return np.mean(diff[1:-1]) extract.mean_second_derivative_central(df["Close"])  #### (5) Volatility Volatility is a statistical measure of the dispersion of a time-series. (i) Variance Larger than Standard Deviation #-> In Package def variance_larger_than_standard_deviation(x): y = np.var(x) return y > np.sqrt(y) extract.variance_larger_than_standard_deviation(df["Close"])  (ii) Variability Index Variability Index is a way to measure how smooth or 'variable' a time series is. var_index_param = {"Volume":df["Volume"].values, "Open": df["Open"].values} @set_property("fctype", "combiner") @set_property("custom", True) def var_index(time,param=var_index_param): final = [] keys = [] for key, magnitude in param.items(): w = 1.0 / np.power(np.subtract(time[1:], time[:-1]), 2) w_mean = np.mean(w) N = len(time) sigma2 = np.var(magnitude) S1 = sum(w * (magnitude[1:] - magnitude[:-1]) ** 2) S2 = sum(w) eta_e = (w_mean * np.power(time[N - 1] - time[0], 2) * S1 / (sigma2 * S2 * N ** 2)) final.append(eta_e) keys.append(key) return {"Interact__{}".format(k): eta_e for eta_e, k in zip(final,keys) } extract.var_index(df["Close"].values,var_index_param)  #### (6) Shape Features that emphasises a particular shape not ordinarily considered as a distribution statistic. Extends to derivations of the original time series too For example a feature looking at the sinusoidal shape of an autocorrelation plot. (i) Symmetrical Boolean variable denoting if the distribution of x looks symmetric. #-> In Package def symmetry_looking(x, param=[{"r": 0.2}]): if not isinstance(x, (np.ndarray, pd.Series)): x = np.asarray(x) mean_median_difference = np.abs(np.mean(x) - np.median(x)) max_min_difference = np.max(x) - np.min(x) return [("r_{}".format(r["r"]), mean_median_difference < (r["r"] * max_min_difference)) for r in param] extract.symmetry_looking(df["Close"])  #### (7) Occurrence Looking at the occurrence, and reoccurence of defined values. (i) Has Duplicate Max #-> In Package def has_duplicate_max(x): """ Checks if the maximum value of x is observed more than once :param x: the time series to calculate the feature of :type x: numpy.ndarray :return: the value of this feature :return type: bool """ if not isinstance(x, (np.ndarray, pd.Series)): x = np.asarray(x) return np.sum(x == np.max(x)) >= 2 extract.has_duplicate_max(df["Close"])  #### (8) Autocorrelation Autocorrelation, also known as serial correlation, is the correlation of a signal with a delayed copy of itself as a function of delay. (i) Partial Autocorrelation Partial autocorrelation is a summary of the relationship between an observation in a time series with observations at prior time steps with the relationships of intervening observations removed. #-> In Package from statsmodels.tsa.stattools import acf, adfuller, pacf def partial_autocorrelation(x, param=[{"lag": 1}]): # Check the difference between demanded lags by param and possible lags to calculate (depends on len(x)) max_demanded_lag = max([lag["lag"] for lag in param]) n = len(x) # Check if list is too short to make calculations if n <= 1: pacf_coeffs = [np.nan] * (max_demanded_lag + 1) else: if (n <= max_demanded_lag): max_lag = n - 1 else: max_lag = max_demanded_lag pacf_coeffs = list(pacf(x, method="ld", nlags=max_lag)) pacf_coeffs = pacf_coeffs + [np.nan] * max(0, (max_demanded_lag - max_lag)) return [("lag_{}".format(lag["lag"]), pacf_coeffs[lag["lag"]]) for lag in param] extract.partial_autocorrelation(df["Close"])  #### (9) Stochasticity Stochastic refers to a randomly determined process. Any features trying to capture stochasticity by degree or type are included under this branch. (i) Augmented Dickey Fuller The Augmented Dickey-Fuller test is a hypothesis test which checks whether a unit root is present in a time series sample. #-> In Package def augmented_dickey_fuller(x, param=[{"attr": "teststat"}]): res = None try: res = adfuller(x) except LinAlgError: res = np.NaN, np.NaN, np.NaN except ValueError: # occurs if sample size is too small res = np.NaN, np.NaN, np.NaN except MissingDataError: # is thrown for e.g. inf or nan in the data res = np.NaN, np.NaN, np.NaN return [('attr_"{}"'.format(config["attr"]), res[0] if config["attr"] == "teststat" else res[1] if config["attr"] == "pvalue" else res[2] if config["attr"] == "usedlag" else np.NaN) for config in param] extract.augmented_dickey_fuller(df["Close"])  #### (10) Averages (i) Median of Magnitudes Skew @set_property("fctype", "simple") @set_property("custom", True) def gskew(x): interpolation="nearest" median_mag = np.median(x) F_3_value = np.percentile(x, 3, interpolation=interpolation) F_97_value = np.percentile(x, 97, interpolation=interpolation) skew = (np.median(x[x <= F_3_value]) + np.median(x[x >= F_97_value]) - 2 * median_mag) return skew extract.gskew(df["Close"])  (ii) Stetson Mean An iteratively weighted mean used in the Stetson variability index stestson_param = {"weight":100., "alpha":2., "beta":2., "tol":1.e-6, "nmax":20} @set_property("fctype", "combiner") @set_property("custom", True) def stetson_mean(x, param=stestson_param): weight= stestson_param["weight"] alpha= stestson_param["alpha"] beta = stestson_param["beta"] tol= stestson_param["tol"] nmax= stestson_param["nmax"] mu = np.median(x) for i in range(nmax): resid = x - mu resid_err = np.abs(resid) * np.sqrt(weight) weight1 = weight / (1. + (resid_err / alpha)**beta) weight1 /= weight1.mean() diff = np.mean(x * weight1) - mu mu += diff if (np.abs(diff) < tol*np.abs(mu) or np.abs(diff) < tol): break return mu extract.stetson_mean(df["Close"])  #### (11) Size (i) Lenght #-> In Package def length(x): return len(x) extract.length(df["Close"])  #### (12) Count (i) Count Above Mean Returns the number of values in x that are higher than the mean of x #-> In Package def count_above_mean(x): m = np.mean(x) return np.where(x > m)[0].size extract.count_above_mean(df["Close"])  #### (13) Streaks (i) Longest Strike Below Mean Returns the length of the longest consecutive subsequence in x that is smaller than the mean of x #-> In Package import itertools def get_length_sequences_where(x): if len(x) == 0: return [0] else: res = [len(list(group)) for value, group in itertools.groupby(x) if value == 1] return res if len(res) > 0 else [0] def longest_strike_below_mean(x): if not isinstance(x, (np.ndarray, pd.Series)): x = np.asarray(x) return np.max(get_length_sequences_where(x <= np.mean(x))) if x.size > 0 else 0 extract.longest_strike_below_mean(df["Close"])  (ii) Wozniak This is an astronomical feature, we count the number of three consecutive data points that are brighter or fainter than$2σ$and normalize the number by$N−2$woz_param = [{"consecutiveStar": n} for n in [2, 4]] @set_property("fctype", "combiner") @set_property("custom", True) def wozniak(magnitude, param=woz_param): iters = [] for consecutiveStar in [stars["consecutiveStar"] for stars in param]: N = len(magnitude) if N < consecutiveStar: return 0 sigma = np.std(magnitude) m = np.mean(magnitude) count = 0 for i in range(N - consecutiveStar + 1): flag = 0 for j in range(consecutiveStar): if(magnitude[i + j] > m + 2 * sigma or magnitude[i + j] < m - 2 * sigma): flag = 1 else: flag = 0 break if flag: count = count + 1 iters.append(count * 1.0 / (N - consecutiveStar + 1)) return [("consecutiveStar_{}".format(config["consecutiveStar"]), iters[en] ) for en, config in enumerate(param)] extract.wozniak(df["Close"])  #### (14) Location (i) Last location of Maximum Returns the relative last location of the maximum value of x. last_location_of_minimum(x), #-> In Package def last_location_of_maximum(x): x = np.asarray(x) return 1.0 - np.argmax(x[::-1]) / len(x) if len(x) > 0 else np.NaN extract.last_location_of_maximum(df["Close"])  #### (15) Model Coefficients Any coefficient that are obtained from a model that might help in the prediction problem. For example here we might include coefficients of polynomial$h(x)$, which has been fitted to the deterministic dynamics of Langevin model. (i) FFT Coefficient Calculates the fourier coefficients of the one-dimensional discrete Fourier Transform for real input. #-> In Package def fft_coefficient(x, param = [{"coeff": 10, "attr": "real"}]): assert min([config["coeff"] for config in param]) >= 0, "Coefficients must be positive or zero." assert set([config["attr"] for config in param]) <= set(["imag", "real", "abs", "angle"]), \ 'Attribute must be "real", "imag", "angle" or "abs"' fft = np.fft.rfft(x) def complex_agg(x, agg): if agg == "real": return x.real elif agg == "imag": return x.imag elif agg == "abs": return np.abs(x) elif agg == "angle": return np.angle(x, deg=True) res = [complex_agg(fft[config["coeff"]], config["attr"]) if config["coeff"] < len(fft) else np.NaN for config in param] index = [('coeff_{}__attr_"{}"'.format(config["coeff"], config["attr"]),res[0]) for config in param] return index extract.fft_coefficient(df["Close"])  (ii) AR Coefficient This feature calculator fits the unconditional maximum likelihood of an autoregressive AR(k) process. #-> In Package from statsmodels.tsa.ar_model import AR def ar_coefficient(x, param=[{"coeff": 5, "k": 5}]): calculated_ar_params = {} x_as_list = list(x) calculated_AR = AR(x_as_list) res = {} for parameter_combination in param: k = parameter_combination["k"] p = parameter_combination["coeff"] column_name = "k_{}__coeff_{}".format(k, p) if k not in calculated_ar_params: try: calculated_ar_params[k] = calculated_AR.fit(maxlag=k, solver="mle").params except (LinAlgError, ValueError): calculated_ar_params[k] = [np.NaN]*k mod = calculated_ar_params[k] if p <= k: try: res[column_name] = mod[p] except IndexError: res[column_name] = 0 else: res[column_name] = np.NaN return [(key, value) for key, value in res.items()] extract.ar_coefficient(df["Close"])  #### (16) Quantiles This includes finding normal quantile values in the series, but also quantile derived measures like change quantiles and index max quantiles. (i) Index Mass Quantile The relative index$i$where$q%$of the mass of the time series$x$lie left of$i$. #-> In Package def index_mass_quantile(x, param=[{"q": 0.3}]): x = np.asarray(x) abs_x = np.abs(x) s = sum(abs_x) if s == 0: # all values in x are zero or it has length 0 return [("q_{}".format(config["q"]), np.NaN) for config in param] else: # at least one value is not zero mass_centralized = np.cumsum(abs_x) / s return [("q_{}".format(config["q"]), (np.argmax(mass_centralized >= config["q"])+1)/len(x)) for config in param] extract.index_mass_quantile(df["Close"])  #### (17) Peaks (i) Number of CWT Peaks This feature calculator searches for different peaks in x. from scipy.signal import cwt, find_peaks_cwt, ricker, welch cwt_param = [ka for ka in [2,6,9]] @set_property("fctype", "combiner") @set_property("custom", True) def number_cwt_peaks(x, param=cwt_param): return [("CWTPeak_{}".format(n), len(find_peaks_cwt(vector=x, widths=np.array(list(range(1, n + 1))), wavelet=ricker))) for n in param] extract.number_cwt_peaks(df["Close"])  #### (18) Density The density, and more specifically the power spectral density of the signal describes the power present in the signal as a function of frequency, per unit frequency. (i) Cross Power Spectral Density This feature calculator estimates the cross power spectral density of the time series$x$at different frequencies. #-> In Package def spkt_welch_density(x, param=[{"coeff": 5}]): freq, pxx = welch(x, nperseg=min(len(x), 256)) coeff = [config["coeff"] for config in param] indices = ["coeff_{}".format(i) for i in coeff] if len(pxx) <= np.max(coeff): # There are fewer data points in the time series than requested coefficients # filter coefficients that are not contained in pxx reduced_coeff = [coefficient for coefficient in coeff if len(pxx) > coefficient] not_calculated_coefficients = [coefficient for coefficient in coeff if coefficient not in reduced_coeff] # Fill up the rest of the requested coefficients with np.NaNs return zip(indices, list(pxx[reduced_coeff]) + [np.NaN] * len(not_calculated_coefficients)) else: return pxx[coeff].ravel()[0] extract.spkt_welch_density(df["Close"])  #### (19) Linearity Any measure of linearity that might make use of something like the linear least-squares regression for the values of the time series. This can be against the time series minus one and many other alternatives. (i) Linear Trend Time Wise Calculate a linear least-squares regression for the values of the time series versus the sequence from 0 to length of the time series minus one. from scipy.stats import linregress #-> In Package def linear_trend_timewise(x, param= [{"attr": "pvalue"}]): ix = x.index # Get differences between each timestamp and the first timestamp in seconds. # Then convert to hours and reshape for linear regression times_seconds = (ix - ix[0]).total_seconds() times_hours = np.asarray(times_seconds / float(3600)) linReg = linregress(times_hours, x.values) return [("attr_\"{}\"".format(config["attr"]), getattr(linReg, config["attr"])) for config in param] extract.linear_trend_timewise(df["Close"])  #### (20) Non-Linearity (i) Schreiber Non-Linearity #-> In Package def c3(x, lag=3): if not isinstance(x, (np.ndarray, pd.Series)): x = np.asarray(x) n = x.size if 2 * lag >= n: return 0 else: return np.mean((_roll(x, 2 * -lag) * _roll(x, -lag) * x)[0:(n - 2 * lag)]) extract.c3(df["Close"])  #### (21) Entropy Any feature looking at the complexity of a time series. This is typically used in medical signal disciplines (EEG, EMG). There are multiple types of measures like spectral entropy, permutation entropy, sample entropy, approximate entropy, Lempel-Ziv complexity and other. This includes entropy measures and there derivations. (i) Binned Entropy Bins the values of x into max_bins equidistant bins. #-> In Package def binned_entropy(x, max_bins=10): if not isinstance(x, (np.ndarray, pd.Series)): x = np.asarray(x) hist, bin_edges = np.histogram(x, bins=max_bins) probs = hist / x.size return - np.sum(p * np.math.log(p) for p in probs if p != 0) extract.binned_entropy(df["Close"])  (ii) SVD Entropy SVD entropy is an indicator of the number of eigenvectors that are needed for an adequate explanation of the data set. svd_param = [{"Tau": ta, "DE": de} for ta in [4] for de in [3,6]] def _embed_seq(X,Tau,D): N =len(X) if D * Tau > N: print("Cannot build such a matrix, because D * Tau > N") exit() if Tau<1: print("Tau has to be at least 1") exit() Y= np.zeros((N - (D - 1) * Tau, D)) for i in range(0, N - (D - 1) * Tau): for j in range(0, D): Y[i][j] = X[i + j * Tau] return Y @set_property("fctype", "combiner") @set_property("custom", True) def svd_entropy(epochs, param=svd_param): axis=0 final = [] for par in param: def svd_entropy_1d(X, Tau, DE): Y = _embed_seq(X, Tau, DE) W = np.linalg.svd(Y, compute_uv=0) W /= sum(W) # normalize singular values return -1 * np.sum(W * np.log(W)) Tau = par["Tau"] DE = par["DE"] final.append(np.apply_along_axis(svd_entropy_1d, axis, epochs, Tau, DE).ravel()[0]) return [("Tau_\"{}\"__De_{}\"".format(par["Tau"], par["DE"]), final[en]) for en, par in enumerate(param)] extract.svd_entropy(df["Close"].values)  (iii) Hjort The Complexity parameter represents the change in frequency. The parameter compares the signal's similarity to a pure sine wave, where the value converges to 1 if the signal is more similar. def _hjorth_mobility(epochs): diff = np.diff(epochs, axis=0) sigma0 = np.std(epochs, axis=0) sigma1 = np.std(diff, axis=0) return np.divide(sigma1, sigma0) @set_property("fctype", "simple") @set_property("custom", True) def hjorth_complexity(epochs): diff1 = np.diff(epochs, axis=0) diff2 = np.diff(diff1, axis=0) sigma1 = np.std(diff1, axis=0) sigma2 = np.std(diff2, axis=0) return np.divide(np.divide(sigma2, sigma1), _hjorth_mobility(epochs)) extract.hjorth_complexity(df["Close"])  #### (22) Fixed Points Fixed points and equilibria as identified from fitted models. (i) Langevin Fixed Points Largest fixed point of dynamics$max\ {h(x)=0}$estimated from polynomial$h(x)\$ which has been fitted to the deterministic dynamics of Langevin model

#-> In Package
def _estimate_friedrich_coefficients(x, m, r):
assert m > 0, "Order of polynomial need to be positive integer, found {}".format(m)
df = pd.DataFrame({'signal': x[:-1], 'delta': np.diff(x)})
try:
df['quantiles'] = pd.qcut(df.signal, r)
except ValueError:
return [np.NaN] * (m + 1)

quantiles = df.groupby('quantiles')

result = pd.DataFrame({'x_mean': quantiles.signal.mean(), 'y_mean': quantiles.delta.mean()})
result.dropna(inplace=True)

try:
return np.polyfit(result.x_mean, result.y_mean, deg=m)
except (np.linalg.LinAlgError, ValueError):
return [np.NaN] * (m + 1)

def max_langevin_fixed_point(x, r=3, m=30):
coeff = _estimate_friedrich_coefficients(x, m, r)

try:
max_fixed_point = np.max(np.real(np.roots(coeff)))
except (np.linalg.LinAlgError, ValueError):
return np.nan

return max_fixed_point

extract.max_langevin_fixed_point(df["Close"])


#### (23) Amplitude

Features derived from peaked values in either the positive or negative direction.

(i) Willison Amplitude

This feature is defined as the amount of times that the change in the signal amplitude exceeds a threshold.

will_param = [ka for ka in [0.2,3]]

@set_property("fctype", "combiner")
@set_property("custom", True)
def willison_amplitude(X, param=will_param):
return [("Thresh_{}".format(n),np.sum(np.abs(np.diff(X)) >= n)) for n in param]

extract.willison_amplitude(df["Close"])


(ii) Percent Amplitude

Returns the largest distance from the median value, measured as a percentage of the median

perc_param = [{"base":ba, "exponent":exp} for ba in [3,5] for exp in [-0.1,-0.2]]

@set_property("fctype", "combiner")
@set_property("custom", True)
def percent_amplitude(x, param =perc_param):
final = []
for par in param:
linear_scale_data = par["base"] ** (par["exponent"] * x)
y_max = np.max(linear_scale_data)
y_min = np.min(linear_scale_data)
y_med = np.median(linear_scale_data)
final.append(max(abs((y_max - y_med) / y_med), abs((y_med - y_min) / y_med)))

return [("Base_{}__Exp{}".format(pa["base"],pa["exponent"]),fin) for fin, pa in zip(final,param)]

extract.percent_amplitude(df["Close"])


#### (24) Probability

Given the observed distribution of time lags cads, compute the probability that the next observation occurs within time minutes of an arbitrary epoch.

#-> fixes required
import scipy.stats as stats

@set_property("fctype", "combiner")
@set_property("custom", True)
return [("time_{}".format(time), stats.percentileofscore(cads, float(time) / (24.0 * 60.0)) / 100.0) for time in param]



#### (25) Crossings

Calculates the crossing of the series with other defined values or series.

(i) Zero Crossing Derivative

The positioning of the edge point is located at the zero crossing of the first derivative of the filter.

zero_param = [0.01, 8]

@set_property("fctype", "combiner")
@set_property("custom", True)
def zero_crossing_derivative(epochs, param=zero_param):
diff = np.diff(epochs)
norm = diff-diff.mean()
return [("e_{}".format(e), np.apply_along_axis(lambda epoch: np.sum(((epoch[:-5] <= e) & (epoch[5:] > e))), 0, norm).ravel()[0]) for e in param]

extract.zero_crossing_derivative(df["Close"])


#### (26) Fluctuations

These features are again from medical signal sciences, but under this category we would include values such as fluctuation based entropy measures, fluctuation of correlation dynamics, and co-fluctuations.

(i) Detrended Fluctuation Analysis (DFA)

DFA Calculate the Hurst exponent using DFA analysis.

from scipy.stats import kurtosis as _kurt
from scipy.stats import skew as _skew
import numpy as np

@set_property("fctype", "simple")
@set_property("custom", True)
def detrended_fluctuation_analysis(epochs):
def dfa_1d(X, Ave=None, L=None):
X = np.array(X)

if Ave is None:
Ave = np.mean(X)

Y = np.cumsum(X)
Y -= Ave

if L is None:
L = np.floor(len(X) * 1 / (
2 ** np.array(list(range(1, int(np.log2(len(X))) - 4))))
)

F = np.zeros(len(L))  # F(n) of different given box length n

for i in range(0, len(L)):
n = int(L[i])  # for each box length L[i]
if n == 0:
print("time series is too short while the box length is too big")
print("abort")
exit()
for j in range(0, len(X), n):  # for each box
if j + n < len(X):
c = list(range(j, j + n))
# coordinates of time in the box
c = np.vstack([c, np.ones(n)]).T
# the value of data in the box
y = Y[j:j + n]
# add residue in this box
F[i] += np.linalg.lstsq(c, y, rcond=None)[1]
F[i] /= ((len(X) / n) * n)
F = np.sqrt(F)

stacked = np.vstack([np.log(L), np.ones(len(L))])
stacked_t = stacked.T
Alpha = np.linalg.lstsq(stacked_t, np.log(F), rcond=None)

return Alpha[0][0]

return np.apply_along_axis(dfa_1d, 0, epochs).ravel()[0]

extract.detrended_fluctuation_analysis(df["Close"])


#### (27) Information

Closely related to entropy and complexity measures. Any measure that attempts to measure the amount of information from an observable variable is included here.

(i) Fisher Information

Fisher information is a statistical information concept distinct from, and earlier than, Shannon information in communication theory.

def _embed_seq(X, Tau, D):

shape = (X.size - Tau * (D - 1), D)
strides = (X.itemsize, Tau * X.itemsize)
return np.lib.stride_tricks.as_strided(X, shape=shape, strides=strides)

fisher_param = [{"Tau":ta, "DE":de} for ta in [3,15] for de in [10,5]]

@set_property("fctype", "combiner")
@set_property("custom", True)
def fisher_information(epochs, param=fisher_param):
def fisher_info_1d(a, tau, de):
# taken from pyeeg improvements

mat = _embed_seq(a, tau, de)
W = np.linalg.svd(mat, compute_uv=False)
W /= sum(W)  # normalize singular values
FI_v = (W[1:] - W[:-1]) ** 2 / W[:-1]
return np.sum(FI_v)

return [("Tau_{}__DE_{}".format(par["Tau"], par["DE"]),np.apply_along_axis(fisher_info_1d, 0, epochs, par["Tau"], par["DE"]).ravel()[0]) for par in param]

extract.fisher_information(df["Close"])


#### (28) Fractals

In mathematics, more specifically in fractal geometry, a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is measured.

(i) Highuchi Fractal

Compute a Higuchi Fractal Dimension of a time series

hig_para = [{"Kmax": 3},{"Kmax": 5}]

@set_property("fctype", "combiner")
@set_property("custom", True)
def higuchi_fractal_dimension(epochs, param=hig_para):
def hfd_1d(X, Kmax):

L = []
x = []
N = len(X)
for k in range(1, Kmax):
Lk = []
for m in range(0, k):
Lmk = 0
for i in range(1, int(np.floor((N - m) / k))):
Lmk += abs(X[m + i * k] - X[m + i * k - k])
Lmk = Lmk * (N - 1) / np.floor((N - m) / float(k)) / k
Lk.append(Lmk)
L.append(np.log(np.mean(Lk)))
x.append([np.log(float(1) / k), 1])

(p, r1, r2, s) = np.linalg.lstsq(x, L, rcond=None)
return p[0]

return [("Kmax_{}".format(config["Kmax"]), np.apply_along_axis(hfd_1d, 0, epochs, config["Kmax"]).ravel()[0] ) for  config in param]

extract.higuchi_fractal_dimension(df["Close"])


(ii) Petrosian Fractal

Compute a Petrosian Fractal Dimension of a time series.

@set_property("fctype", "simple")
@set_property("custom", True)
def petrosian_fractal_dimension(epochs):
def pfd_1d(X, D=None):
# taken from pyeeg
"""Compute Petrosian Fractal Dimension of a time series from either two
cases below:
1. X, the time series of type list (default)
2. D, the first order differential sequence of X (if D is provided,
recommended to speed up)
In case 1, D is computed using Numpy's difference function.
To speed up, it is recommended to compute D before calling this function
because D may also be used by other functions whereas computing it here
again will slow down.
"""
if D is None:
D = np.diff(X)
D = D.tolist()
N_delta = 0  # number of sign changes in derivative of the signal
for i in range(1, len(D)):
if D[i] * D[i - 1] < 0:
N_delta += 1
n = len(X)
return np.log10(n) / (np.log10(n) + np.log10(n / n + 0.4 * N_delta))
return np.apply_along_axis(pfd_1d, 0, epochs).ravel()[0]

extract.petrosian_fractal_dimension(df["Close"])


#### (29) Exponent

(i) Hurst Exponent

The Hurst exponent is used as a measure of long-term memory of time series. It relates to the autocorrelations of the time series, and the rate at which these decrease as the lag between pairs of values increases.

@set_property("fctype", "simple")
@set_property("custom", True)
def hurst_exponent(epochs):
def hurst_1d(X):

X = np.array(X)
N = X.size
T = np.arange(1, N + 1)
Y = np.cumsum(X)
Ave_T = Y / T

S_T = np.zeros(N)
R_T = np.zeros(N)
for i in range(N):
S_T[i] = np.std(X[:i + 1])
X_T = Y - T * Ave_T[i]
R_T[i] = np.ptp(X_T[:i + 1])

for i in range(1, len(S_T)):
if np.diff(S_T)[i - 1] != 0:
break
for j in range(1, len(R_T)):
if np.diff(R_T)[j - 1] != 0:
break
k = max(i, j)
assert k < 10, "rethink it!"

R_S = R_T[k:] / S_T[k:]
R_S = np.log(R_S)

n = np.log(T)[k:]
A = np.column_stack((n, np.ones(n.size)))
[m, c] = np.linalg.lstsq(A, R_S, rcond=None)[0]
H = m
return H
return np.apply_along_axis(hurst_1d, 0, epochs).ravel()[0]

extract.hurst_exponent(df["Close"])


(ii) Largest Lyauponov Exponent

In mathematics the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectories.

def _embed_seq(X, Tau, D):
shape = (X.size - Tau * (D - 1), D)
strides = (X.itemsize, Tau * X.itemsize)
return np.lib.stride_tricks.as_strided(X, shape=shape, strides=strides)

lyaup_param = [{"Tau":4, "n":3, "T":10, "fs":9},{"Tau":8, "n":7, "T":15, "fs":6}]

@set_property("fctype", "combiner")
@set_property("custom", True)
def largest_lyauponov_exponent(epochs, param=lyaup_param):
def LLE_1d(x, tau, n, T, fs):

Em = _embed_seq(x, tau, n)
M = len(Em)
A = np.tile(Em, (len(Em), 1, 1))
B = np.transpose(A, [1, 0, 2])
square_dists = (A - B) ** 2  # square_dists[i,j,k] = (Em[i][k]-Em[j][k])^2
D = np.sqrt(square_dists[:, :, :].sum(axis=2))  # D[i,j] = ||Em[i]-Em[j]||_2

# Exclude elements within T of the diagonal
band = np.tri(D.shape[0], k=T) - np.tri(D.shape[0], k=-T - 1)
band[band == 1] = np.inf
neighbors = (D + band).argmin(axis=0)  # nearest neighbors more than T steps away

# in_bounds[i,j] = (i+j <= M-1 and i+neighbors[j] <= M-1)
inc = np.tile(np.arange(M), (M, 1))
row_inds = (np.tile(np.arange(M), (M, 1)).T + inc)
col_inds = (np.tile(neighbors, (M, 1)) + inc.T)
in_bounds = np.logical_and(row_inds <= M - 1, col_inds <= M - 1)
# Uncomment for old (miscounted) version
# in_bounds = numpy.logical_and(row_inds < M - 1, col_inds < M - 1)
row_inds[~in_bounds] = 0
col_inds[~in_bounds] = 0

# neighbor_dists[i,j] = ||Em[i+j]-Em[i+neighbors[j]]||_2
J = (~neighbor_dists.mask).sum(axis=1)  # number of in-bounds indices by row
# Set invalid (zero) values to 1; log(1) = 0 so sum is unchanged

neighbor_dists[neighbor_dists == 0] = 1

# !!! this fixes the divide by zero in log error !!!
neighbor_dists.data[neighbor_dists.data == 0] = 1

d_ij = np.sum(np.log(neighbor_dists.data), axis=1)
mean_d = d_ij[J > 0] / J[J > 0]

x = np.arange(len(mean_d))
X = np.vstack((x, np.ones(len(mean_d)))).T
[m, c] = np.linalg.lstsq(X, mean_d, rcond=None)[0]
Lexp = fs * m
return Lexp

return [("Tau_{}__n_{}__T_{}__fs_{}".format(par["Tau"], par["n"], par["T"], par["fs"]), np.apply_along_axis(LLE_1d, 0, epochs, par["Tau"], par["n"], par["T"], par["fs"]).ravel()[0]) for par in param]

extract.largest_lyauponov_exponent(df["Close"])


#### (30) Spectral Analysis

Spectral analysis is analysis in terms of a spectrum of frequencies or related quantities such as energies, eigenvalues, etc.

(i) Whelch Method

The Whelch Method is an approach for spectral density estimation. It is used in physics, engineering, and applied mathematics for estimating the power of a signal at different frequencies.

from scipy import signal, integrate

whelch_param = [100,200]

@set_property("fctype", "combiner")
@set_property("custom", True)
def whelch_method(data, param=whelch_param):

final = []
for Fs in param:
f, pxx = signal.welch(data, fs=Fs, nperseg=1024)
d = {'psd': pxx, 'freqs': f}
df = pd.DataFrame(data=d)
dfs = df.sort_values(['psd'], ascending=False)
rows = dfs.iloc[:10]
final.append(rows['freqs'].mean())

return [("Fs_{}".format(pa),fin) for pa, fin in zip(param,final)]

extract.whelch_method(df["Close"])

#-> Basically same as above
freq_param = [{"fs":50, "sel":15},{"fs":200, "sel":20}]

@set_property("fctype", "combiner")
@set_property("custom", True)
def find_freq(serie, param=freq_param):

final = []
for par in param:
fft0 = np.fft.rfft(serie*np.hanning(len(serie)))
freqs = np.fft.rfftfreq(len(serie), d=1.0/par["fs"])
fftmod = np.array([np.sqrt(fft0[i].real**2 + fft0[i].imag**2) for i in range(0, len(fft0))])
d = {'fft': fftmod, 'freq': freqs}
df = pd.DataFrame(d)
hop = df.sort_values(['fft'], ascending=False)
rows = hop.iloc[:par["sel"]]
final.append(rows['freq'].mean())

return [("Fs_{}__sel{}".format(pa["fs"],pa["sel"]),fin) for pa, fin in zip(param,final)]

extract.find_freq(df["Close"])


#### (31) Percentile

(i) Flux Percentile

Flux (or radiant flux) is the total amount of energy that crosses a unit area per unit time. Flux is an astronomical value, measured in joules per square metre per second (joules/m2/s), or watts per square metre. Here we provide the ratio of flux percentiles.

#-> In Package

import math
def flux_perc(magnitude):
sorted_data = np.sort(magnitude)
lc_length = len(sorted_data)

F_60_index = int(math.ceil(0.60 * lc_length))
F_40_index = int(math.ceil(0.40 * lc_length))
F_5_index = int(math.ceil(0.05 * lc_length))
F_95_index = int(math.ceil(0.95 * lc_length))

F_40_60 = sorted_data[F_60_index] - sorted_data[F_40_index]
F_5_95 = sorted_data[F_95_index] - sorted_data[F_5_index]
F_mid20 = F_40_60 / F_5_95

return {"FluxPercentileRatioMid20": F_mid20}

extract.flux_perc(df["Close"])


#### (32) Range

(i) Range of Cummulative Sum

@set_property("fctype", "simple")
@set_property("custom", True)
def range_cum_s(magnitude):
sigma = np.std(magnitude)
N = len(magnitude)
m = np.mean(magnitude)
s = np.cumsum(magnitude - m) * 1.0 / (N * sigma)
R = np.max(s) - np.min(s)
return {"Rcs": R}

extract.range_cum_s(df["Close"])


#### (33) Structural

Structural features, potential placeholders for future research.

(i) Structure Function

The structure function of rotation measures (RMs) contains information on electron density and magnetic field fluctuations when used i astronomy. It becomes a custom feature when used with your own unique time series data.

from scipy.interpolate import interp1d

struct_param = {"Volume":df["Volume"].values, "Open": df["Open"].values}

@set_property("fctype", "combiner")
@set_property("custom", True)
def structure_func(time, param=struct_param):

dict_final = {}
for key, magnitude in param.items():
dict_final[key] = []
Nsf, Np = 100, 100
sf1, sf2, sf3 = np.zeros(Nsf), np.zeros(Nsf), np.zeros(Nsf)
f = interp1d(time, magnitude)

time_int = np.linspace(np.min(time), np.max(time), Np)
mag_int = f(time_int)

for tau in np.arange(1, Nsf):
sf1[tau - 1] = np.mean(
np.power(np.abs(mag_int[0:Np - tau] - mag_int[tau:Np]), 1.0))
sf2[tau - 1] = np.mean(
np.abs(np.power(
np.abs(mag_int[0:Np - tau] - mag_int[tau:Np]), 2.0)))
sf3[tau - 1] = np.mean(
np.abs(np.power(
np.abs(mag_int[0:Np - tau] - mag_int[tau:Np]), 3.0)))
sf1_log = np.log10(np.trim_zeros(sf1))
sf2_log = np.log10(np.trim_zeros(sf2))
sf3_log = np.log10(np.trim_zeros(sf3))

if len(sf1_log) and len(sf2_log):
m_21, b_21 = np.polyfit(sf1_log, sf2_log, 1)
else:

m_21 = np.nan

if len(sf1_log) and len(sf3_log):
m_31, b_31 = np.polyfit(sf1_log, sf3_log, 1)
else:

m_31 = np.nan

if len(sf2_log) and len(sf3_log):
m_32, b_32 = np.polyfit(sf2_log, sf3_log, 1)
else:

m_32 = np.nan
dict_final[key].append(m_21)
dict_final[key].append(m_31)
dict_final[key].append(m_32)

return [("StructureFunction_{}__m_{}".format(key, name), li)  for key, lis in dict_final.items() for name, li in zip([21,31,32], lis)]

struct_param = {"Volume":df["Volume"].values, "Open": df["Open"].values}

extract.structure_func(df["Close"],struct_param)


#### (34) Distribution

(i) Kurtosis

#-> In Package
def kurtosis(x):

if not isinstance(x, pd.Series):
x = pd.Series(x)
return pd.Series.kurtosis(x)

extract.kurtosis(df["Close"])


(ii) Stetson Kurtosis

@set_property("fctype", "simple")
@set_property("custom", True)
def stetson_k(x):
"""A robust kurtosis statistic."""
n = len(x)
x0 = stetson_mean(x, 1./20**2)
delta_x = np.sqrt(n / (n - 1.)) * (x - x0) / 20
ta = 1. / 0.798 * np.mean(np.abs(delta_x)) / np.sqrt(np.mean(delta_x**2))
return ta

extract.stetson_k(df["Close"])


## (5) Synthesise

Time-Series synthesisation (TSS) happens before the feature extraction step and Cross Sectional Synthesisation (CSS) happens after the feature extraction step. Currently I will only include a CSS package, in the future, I would further work on developing out this section. This area still has a lot of performance and stability issues. In the future it might be a more viable candidate to improve prediction.

from lightgbm import LGBMRegressor
from sklearn.metrics import mean_squared_error

def model(df_final):
model = LGBMRegressor()
train = df_final[~df_final.isin(test)].dropna()
model = model.fit(train.drop(["Close_1"],axis=1),train["Close_1"])
preds = model.predict(test.drop(["Close_1"],axis=1))
train = df_final[~df_final.isin(test)].dropna()
model = model.fit(train.drop(["Close_1"],axis=1),train["Close_1"])
val = mean_squared_error(test["Close_1"],preds);
return val

pip install ctgan

from ctgan import CTGANSynthesizer

#discrete_columns = [""]
ctgan = CTGANSynthesizer()
ctgan.fit(df,epochs=10) #15


Random Benchmark

np.random.seed(1)
df_in = df.copy()
df_in["Close_1"] = np.random.permutation(df_in["Close_1"].values)
model(df_in)


Generated Performance

df_gen = ctgan.sample(len(df_in)*100)
model(df_gen)


As expected a cross-sectional technique, does not work well on time-series data, in the future, other methods will be investigated.

## (6) Skeleton Example

Here I will perform tabular agumenting methods on a small dataset single digit features and around 250 instances. This is not necessarily the best sized dataset to highlight the performance of tabular augmentation as some method like extraction would be overkill as it would lead to dimensionality problems. It is also good to know that there are close to infinite number of ways to perform these augmentation methods. In the future, automated augmentation methods can guide the experiment process.

The approach taken in this skeleton is to develop running models that are tested after each augmentation to highlight what methods might work well on this particular dataset. The metric we will use is mean squared error. In this implementation we do not have special hold-out sets.

The above framework of implementation will be consulted, but one still have to be strategic as to when you apply what function, and you have to make sure that you are processing your data with appropriate techniques (drop null values, fill null values) at the appropriate time.

#### Validation

Develop Model and Define Metric

from lightgbm import LGBMRegressor
from sklearn.metrics import mean_squared_error

def model(df_final):
model = LGBMRegressor()
train = df_final[~df_final.isin(test)].dropna()
model = model.fit(train.drop(["Close_1"],axis=1),train["Close_1"])
preds = model.predict(test.drop(["Close_1"],axis=1))
train = df_final[~df_final.isin(test)].dropna()
model = model.fit(train.drop(["Close_1"],axis=1),train["Close_1"])
val = mean_squared_error(test["Close_1"],preds);
return val


df = data_copy()

model(df)

302.61676570345287


(1) (7) (i) Transformation - Decomposition - Naive

## If Inferred Seasonality is Too Large Default to Five
seasons = transform.infer_seasonality(df["Close"],index=0)
df_out = transform.naive_dec(df.copy(), ["Close","Open"], freq=5)
model(df_out) #improvement

274.34477082783525


(1) (8) (i) Transformation - Filter - Baxter-King-Bandpass

df_out = transform.bkb(df_out, ["Close","Low"])
df_best = df_out.copy()
model(df_out) #improvement

267.1826850968307


(1) (3) (i) Transformation - Differentiation - Fractional

df_out = transform.fast_fracdiff(df_out, ["Close_BPF"],0.5)
model(df_out) #null

267.7083192402742


(1) (1) (i) Transformation - Scaling - Robust Scaler

df_out = df_out.dropna()
df_out = transform.robust_scaler(df_out, drop=["Close_1"])
model(df_out) #noisy

270.96980399571214


(2) (2) (i) Interactions - Operator - Multiplication/Division

df_out.head()

df_out = interact.muldiv(df_out, ["Close","Open_NDDS","Low_BPF"])
model(df_out) #noisy

285.6420643864313

df_r = df_out.copy()


(2) (6) (i) Interactions - Speciality - Technical

import ta
df = interact.tech(df)
df_out = pd.merge(df_out,  df.iloc[:,7:], left_index=True, right_index=True, how="left")


Clean Dataframe and Metric

"""Droping column where missing values are above a threshold"""
df_out = df_out.dropna(thresh = len(df_out)*0.95, axis = "columns")
df_out = df_out.dropna()
df_out = df_out.replace([np.inf, -np.inf], np.nan).ffill().fillna(0)
close = df_out["Close"].copy()
df_d = df_out.copy()
model(df_out) #improve

592.52971755184


(3) (1) (i) Mapping - Eigen Decomposition - PCA

from sklearn.decomposition import PCA, IncrementalPCA, KernelPCA

df_out = transform.robust_scaler(df_out, drop=["Close_1"])

df_out = df_out.replace([np.inf, -np.inf], np.nan).ffill().fillna(0)
df_out = mapper.pca_feature(df_out, drop_cols=["Close_1"], variance_or_components=0.9, n_components=8,non_linear=False)

model(df_out) #noisy but not too bad given the 10 fold dimensionality reduction

687.158330455884


(4) Extracting

Here at first, I show the functions that have been added to the DeltaPy fork of tsfresh. You have to add your own personal adjustments based on the features you would like to construct. I am using self-developed features, but you can also use TSFresh's community functions.

The following files have been appropriately ammended (Get in contact for advice)

(4) (10) (i) Extracting - Averages - GSkew

extract.gskew(df_out["PCA_1"])

-0.7903067336449059


(4) (21) (ii) Extracting - Entropy - SVD Entropy

svd_param = [{"Tau": ta, "DE": de}
for ta in [4]
for de in [3,6]]

extract.svd_entropy(df_out["PCA_1"],svd_param)

[('Tau_"4"__De_3"', 0.7234823323374294),
('Tau_"4"__De_6"', 1.3014347840145244)]


(4) (13) (ii) Extracting - Streaks - Wozniak

woz_param = [{"consecutiveStar": n} for n in [2, 4]]

extract.wozniak(df_out["PCA_1"],woz_param)

[('consecutiveStar_2', 0.012658227848101266), ('consecutiveStar_4', 0.0)]


(4) (28) (i) Extracting - Fractal - Higuchi

hig_param = [{"Kmax": 3},{"Kmax": 5}]

extract.higuchi_fractal_dimension(df_out["PCA_1"],hig_param)

[('Kmax_3', 0.577913816027104), ('Kmax_5', 0.8176960510304725)]


(4) (5) (ii) Extracting - Volatility - Variability Index

var_index_param = {"Volume":df["Volume"].values, "Open": df["Open"].values}

extract.var_index(df["Close"].values,var_index_param)

{'Interact__Open': 0.00396022538846289,
'Interact__Volume': 0.20550155114176533}


Time Series Extraction

pip install git+git://github.com/firmai/tsfresh.git

#Construct the preferred input dataframe.
from tsfresh.utilities.dataframe_functions import roll_time_series
df_out["ID"] = 0
periods = 30
df_out = df_out.reset_index()
df_ts = roll_time_series(df_out,"ID","Date",None,1,periods)
counts = df_ts['ID'].value_counts()
df_ts = df_ts[df_ts['ID'].isin(counts[counts > periods].index)]

#Perform extraction
from tsfresh.feature_extraction import extract_features, CustomFCParameters
settings_dict = CustomFCParameters()
settings_dict["var_index"] = {"PCA_1":None, "PCA_2": None}
df_feat = extract_features(df_ts.drop(["Close_1"],axis=1),default_fc_parameters=settings_dict,column_id="ID",column_sort="Date")

Feature Extraction: 100%|██████████| 5/5 [00:10<00:00,  2.14s/it]

# Cleaning operations
import pandasvault as pv
df_feat2 = df_feat.copy()
df_feat = df_feat.dropna(thresh = len(df_feat)*0.50, axis = "columns")
df_feat_cons = pv.constant_feature_detect(data=df_feat,threshold=0.9)
df_feat = df_feat.drop(df_feat_cons, axis=1)
df_feat = df_feat.ffill()
df_feat = pd.merge(df_feat,df[["Close_1"]],left_index=True,right_index=True,how="left")
print(df_feat.shape)
model(df_feat) #noisy

7  variables are found to be almost constant
(208, 48)
2064.7813982935995

from tsfresh import select_features
from tsfresh.utilities.dataframe_functions import impute

impute(df_feat)
df_feat_2 = select_features(df_feat.drop(["Close_1"],axis=1),df_feat["Close_1"],fdr_level=0.05)
df_feat_2["Close_1"] = df_feat["Close_1"]
model(df_feat_2) #improvement (b/ not an augmentation method)

1577.5273071299482


(3) (6) (i) Feature Agglomoration;   (1)(2)(i) Standard Scaler.

Like in this step, after (1), (2), (3), (4) and (5), you can often circle back to the initial steps to normalise the data and dimensionally reduce the data for the final model.

import numpy as np
from sklearn import datasets, cluster

def feature_agg(df, drop, components):
components = min(df.shape[1]-1,components)
agglo = cluster.FeatureAgglomeration(n_clusters=components,)
df = df.drop(drop,axis=1)
agglo.fit(df)
df = pd.DataFrame(agglo.transform(df))

return df

df_final = transform.standard_scaler(df_feat_2, drop=["Close_1"])
df_final = mapper.feature_agg(df_final,["Close_1"],4)
df_final.index = df_feat.index
df_final["Close_1"] = df_feat["Close_1"]
model(df_final) #noisy

1949.89085894338


Final Model After Applying 13 Arbitrary Augmentation Techniques

model(df_final) #improvement

1949.89085894338


Original Model Before Augmentation

df_org = df.iloc[:,:7][df.index.isin(df_final.index)]
model(df_org)

389.783990984133


Best Model After Developing 8 Augmenting Features

df_best = df_best.replace([np.inf, -np.inf], np.nan).ffill().fillna(0)
model(df_best)

267.1826850968307


Commentary

There are countless ways in which the current model can be improved, this can take on an automated process where all techniques are tested against a hold out set, for example, we can perform the operation below, and even though it improves the score here, there is a need for more robust tests. The skeleton example above is not meant to highlight the performance of the package. It simply serves as an example of how one can go about applying augmentation methods.

Quite naturally this example suffers from dimensionality issues with array shapes reaching (208, 48), furthermore you would need a sample that is at least 50-100 times larger before machine learning methods start to make sense.

Nonetheless, in this example, Transformation, Interactions and Mappings (applied to extraction output) performed fairly well. Extraction augmentation was overkill, but created a reasonable model when dimensionally reduced. A better selection of one of the 50+ augmentation methods and the order of augmentation could further help improve the outcome if robustly tested against development sets.

[1] DeltaPy Development

Author: firmai
Source Code: https://github.com/firmai/deltapy

#engineering

1619522210

## 5 Top Web Design and Development Tips for an Awesome Web App

First impression is the last impression. This statement is absolutely correct when we talk about web design and development. In this blog, let us talk about the tips for a great web web app.

Web application development has come a long way since the beginning of the World Wide Web. The web environment today uses HTML and CSS to view data and content to users while JavaScript is used to interact with the client.

Did you know that when a visitor arrives on your website, you have about five seconds (or less) to capture their attention and keep them where they are? That’s not a whole lot of time to impress someone, so if your load time is not perfect or your site’s navigation is all over the place, you can say goodbye to your visitors.

Believe it or not, the rapidly changing world of technology is not helping with this, either. New trends can easily make your website outdated and render it all but useless, leaving you with fewer visitors than you started with.

So, now the below questions arise:

How are you supposed to fix this issue and keep your visitors?

How do you create a website that looks good, functions perfectly, and communicates your message clearly?

Developers and designers have various approaches to improve web design. Regardless of whether you have a perfect, smooth, and proficient site, that doesn’t mean it will suitable always.

You ought to consistently consider site improvement thoughts as time passes by.

Web design company in India

#web-design-tips #web-designing-tips #website-design-tips #website-designing-tips #web-development-tips

1594381140

## Using Permission and Perception to Change the Brand Experience

For a few weeks during the Coronavirus’ spread across the United States, Americans all spoke the same language.

Phrases like “flatten the curve” and “social distancing” entered our lexicon. Many have documented our new set of social norms, from stepping away from strangers on the street (once awkward, now thoughtful) to wearing a mask in public (once suspicious, now a sign of good citizenship).

But then these shared standards began taking on political connotations.

As government officials split over next steps in the battle against the virus, Americans fell back into factions, now perhaps easier to distinguish than ever. Those who stepped away from strangers on the street and those who didn’t; those who wore masks and those who wouldn’t.

Stores became battlegrounds for this changing, charged environment. Customers at Costco and Gelson’s filmed seething cell phone videos in response to mandatory mask policies, which quickly went viral. For some viewers, these moments became cause to support the brands, while others pledged to cancel their memberships.

By simply following government orders or recommendations, these companies made an inadvertent political statement, entering into a heated cultural conversation.

And yet, this is just another proof point that our societal frameworks are changing.

When societal frameworks shift, your brand’s actions are perceived through a different lens.

As Scott Galloway heralded in 2018 after Nike made Colin Kaepernick the face of their 30-year anniversary “Just Do It” ad campaign, our leadership has politicized sports — the last “oasis” of politics-free discourse — and has since then upped the ante in making everyday acts partisan in nature.

This is likely a reality that we can never revert away from again.

In moments of crisis, brands attempting to reestablish their commitment to consumers face a particular challenge, one that can easily go awry if you don’t pay attention to the societal framework shaping our choices.

There is a subtext to every move, an implicit bias or belief to every action. Brand perceptions don’t just come from words or actions — they come from reading between the lines.

That means you can’t make brand choices in a bubble. You need to consider the culture and the belief systems that those choices live within.

So, let’s look at some of the implicit forces at play.

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