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Guide to Time Series Analysis with Python — 3: Autoregressive Process

Buse Köseoğlu
4 min readAug 7, 2023

In the previous article, we examined the moving average process. This time we will examine another statistical model, the autoregressive process.

You can find previous articles below.
1.Guide to Time Series Analysis with Python — 1: Analysis Techniques and Baseline Model

2.Guide to Time Series Analysis with Python — 2: Moving Average Process

If you’re ready, let’s start.

What is Autoregressive Process (AR)?

Autoregressive process is a statistical model used for time series to predict the future by looking at historical data. Just as the moving average process uses the effect of past errors, the autoregressive process says that the past values in the time series affect the present. We can see how this is used in the equation below. Here, the parameter we want to determine is the “p” parameter. This p-value decides how far back we go. It is important to find the optimum number.

Specifying the p Parameter

We use a method like the method in the moving average process to determine this parameter. But this time we will use PACF (Partial Autocorrelation Function) plot instead of ACF plot. PACF gives the partial correlation of the time series with its lagged values.
If we examine the roadmap below, we can see how we can reach the result step by step. Here, first of all, we need to see…

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