Constrain the Model Selection Set
TimeSeriesModelFit allows you to automate selection from a given family of models or from a given range of models, as well as to fix integration order or seasonality.
Generate data with small seasonality.
Use TimeSeriesModelFit to automatically find the most suitable time series model.
Based on variances of parameter estimators, the second and the third autoregressive coefficients are not significantly different from zero, suggesting possible seasonality of 4.
Confirm the seasonality guess with the plot of the sample partial correlation function.
Restrict the search to seasonal ARMA family with seasonality of 4.
Compare with fitting longer autoregressive models.
Both the Bayesian information criterion and the Akaike information criterion favor the seasonal model.