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.

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Use TimeSeriesModelFit to automatically find the most suitable time series model.

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Based on variances of parameter estimators, the second and the third autoregressive coefficients are not significantly different from zero, suggesting possible seasonality of 4.

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Confirm the seasonality guess with the plot of the sample partial correlation function.

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Restrict the search to seasonal ARMA family with seasonality of 4.

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Compare with fitting longer autoregressive models.

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Both the Bayesian information criterion and the Akaike information criterion favor the seasonal model.

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