In this article, primarily I share my experience in understanding the ACF, PACF plots, and their significance in selecting the order of ARMA models.

Selecting candidate **Auto Regressive Moving Average * (ARMA) models for time series analysis and forecasting, understanding *Autocorrelation function** (ACF), and

**ACF plot** is a bar chart of coefficients of correlation between a time series and it lagged values. Simply stated: ACF explains how the present value of a given time series is correlated with the past (1-unit past, 2-unit past, …, n-unit past) values. In the ACF plot, the x-axis expresses the correlation coefficient whereas the y-axis mentions the number of lags. Assume that, y(t-1)

*y(t), y(t-1),….y(t-n)* are values of a time series at time *t, t-1,…,t-n,* then the lag-1 value is the correlation coefficient between *y(t)* and *y(t-1)*, lag-2 is the correlation coefficient between *y(t)* and *y(t-2)* and so on.

**PACF** is the partial autocorrelation function that explains the partial correlation between the series and lags of itself. In simple terms, PACF can be explained using a linear regression where we predict *y(t)* from *y(t-1), y(t-2),* and *y(t-3)* [2]. In PACF, we correlate the “parts” of *y(t)* and *y(t-3)* that are not predicted by *y(t-1)* and *y(t-2)* .

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