My question is, if a model allows the errors to follow an AR(1) process, how to check for the model adequacy? Can we use ACF and PACF plots?
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$\begingroup$ Related: stats.stackexchange.com/questions/560778 $\endgroup$– Richard HardyCommented Jan 18, 2022 at 18:54
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The parameters of the ARIMA model are defined as follows:
p: The number of lag observations included in the model, also called the lag order.
d: The number of times that the raw observations are differenced, also called the degree of differencing.
q: The size of the moving average window, also called the order of moving average.
How do we decide these variables?
Apply differencing to time series and seasonal difference if needed to reach stationarity to get an estimate for d and D values.
Plot the Autocorrelation and Partial Autocorrelation plots to help you estimate the p, P, and q, Q values.
Fine-tune the model if needed changing the parameters according to the general rules of ARIMA. Another option would be cross-validation with a list of parameters until you find a model retuning a sufficiently low AIC score.
For more detailed info on the interpretation of these model hyper-parameters and their relation to the Autocorrelation and PACF plots, this was super helpful: https://people.duke.edu/~rnau/411arim3.htm
