# An intuitive guide to differencing time series in Python

In this article, I will do my best to provide a simple and easy on the maths introduction to the theory. Then, I will also show two different approaches you can follow in Python.

While working with time series, sooner or later you will encounter the term differencing. In this article, I will do my best to provide a simple and easy on the maths introduction to the theory. Then, I will also show two different approaches you can follow in Python. Let’s start.

## Theory

Before I actually explain what differencing is, I need to quickly introduce another concept which is crucial when working with time series data — stationarity. There are quite a few great articles out there going deeply into what stationarity is, including the distinction between weak and strong variants, etc. However, for the sake of this article, we will focus on a very basic definition.

It all comes around the fact that time series data is different from other kinds of data you can encounter while working with regression problems, for example, predicting the price of houses in the Boston area. That is because time series are characterized by temporal structure, what in practice means that the order of the data points actually does matter.

To give some examples, time series data can exhibit a trend (an increasing and/or decreasing pattern, for example, in production of some goods or in sales) or seasonality (when some time periods exhibit different patterns, for example, increased tourism-related income during summer months). From the statistical side, a trend means varying mean over time, while seasonality hints at varying variance. In such a case, we are dealing with non-stationary series.

So a stationary series is basically a time series that has stable/constant statistical properties (mean, variance, etc.) over time. Or in other words, the observations in such time series are not dependent on time. And why do we care about that? Simply, it is much easier to work with such series and make accurate predictions. Some approaches to time series modeling either assume or require the underlying time series to be stationary.

I will leave out the details on testing for stationarity (for example, with the Augmented Dickey-Fuller test) for another article and come right back to the main topic — differencing. Differencing is one of the possible methods of dealing with non-stationary data and it is used for trying to make such a series stationary. In practice, it means subtracting subsequent observations from one another, following the formula:

`diff(t) = x(t) — x(t — 1)`

where `diff` is the differenced series at time t and `x` stands for an observation of the original series. The transformation is simple enough, but I will illustrate some small nuances in the practical example below.

## Sktime: a Unified Python Library for Time Series Machine Learning

The “sklearn” for time series forecasting, classification, and regression. Existing tools are not well-suited to time series tasks and do not easily integrate together. Methods in the scikit-learn package assume that data is structured in a tabular format and each column is i.i.d. — assumptions that do not hold for time series data.

## What is Time Series Forecasting?

In this article, we will be discussing an algorithm that helps us analyze past trends and lets us focus on what is to unfold next so this algorithm is time series forecasting. In this analysis, you have one variable -TIME. A time series is a set of observations taken at a specified time usually equal in intervals. It is used to predict future value based on previously observed data points.

## Time Series Analysis using Pandas in Python

Bonus intro to keywords like seasonality, trend, autocorrelation, and much more.

## Learn Time Series Forecasting | Time Series Analysis With Python

Learn Time Series Forecasting | Time Series Analysis With Python will help you to master all the concepts of time series. Time series analysis is a statistical technique to analyze the pattern of data points taken over time to forecast the future. It is an essential technique in data science and predictive modeling and that is why people skilled in time series analysis and forecasting are in huge demand right now.

## My Time Series Toolkit

My models of choice for time series analysis. When it comes to time series forecasting, I’m a great believer that the simpler the model, the better.