I want to select lag (AR model order) for the series Food price inflation.
AIC gives 4.
SIC gives 3.
And also, I print its PACF plot.
How can I interpret the PACF plot to select the correct lag?
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2$\begingroup$ "The correct lag" is a very slippery concept. Simulate a couple of AR($p$) time series for different values of $p$ and ask time series analysis to fit an AR model to each one; I would be surprised if a majority got the original AR order. And that is a situation where the true data generating process actually is AR. For food prices, I would absolutely expect extraneous dynamics... so restricting our search space to AR models means that we already miss the true DGP. $\endgroup$– Stephan KolassaCommented Jun 20 at 23:08
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1$\begingroup$ That said, I would definitely go with information criteria. If AIC says AR(4) and SIC says AR(3), then likely enough both are very close together, and the forecasts will look extremely similar. Just take the average of the two forecasts, and you will likely outperform either one. People have been playing with weighted averaging in such a case (Kolassa, 2011), but it does not really outperform unweighted averages (the "forecast combination puzzle"). $\endgroup$– Stephan KolassaCommented Jun 20 at 23:11
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$\begingroup$ well, what does the pact plot indicates? I don't know how to Interpret these plots? @StephanKolassa thank you for informing me. $\endgroup$– 1190Commented Jun 20 at 23:20
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$\begingroup$ Is the first bar due to lag 1 or lag 0? If lag 1, this looks like AR(3). $\endgroup$– Richard HardyCommented Jun 21 at 6:11
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$\begingroup$ Lags at 13/14 are interesting in the domain. Maybe "next paycheck" purchasing or a bi-monthly paycheck cadence? Having period sine/cosines can help machine learners pick up cyclic/seasonality phenomena. $\endgroup$– EngrStudentCommented Jun 27 at 16:59
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