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ARIMA (AutoRegressive Integrated Moving Average) is a popular time series forecasting method that models a time series as a combination of autoregressive (AR) and moving average (MA) components, with the added ability to handle non-stationary time series through differencing.

Let’s consider an example of forecasting the monthly sales of a particular product over the past 2 years, from January 2019 to December 2020. Here is the data:

Month Sales
Jan-19 100
Feb-19 120
Mar-19 125
Apr-19 130
May-19 140
Jun-19 145
Jul-19 150
Aug-19 155
Sep-19 160
Oct-19 170
Nov-19 180
Dec-19 200
Jan-20 210
Feb-20 220
Mar-20 230
Apr-20 240
May-20 250
Jun-20 260
Jul-20 270
Aug-20 280
Sep-20 290
Oct-20 300
Nov-20 310
Dec-20 320

We want to build an ARIMA model to forecast the sales for the next 6 months (Jan-21 to Jun-21).

First, we need to check if the time series is stationary. Stationarity is a key assumption of ARIMA models. A stationary time series has a constant mean, variance, and autocorrelation over time. We can check for stationarity using a statistical test like the Augmented Dickey-Fuller (ADF) test. Here’s the Python code to perform the test:

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