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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X BlockRandom[SeedRandom["Mathematica10"]; data = RandomFunction[ SARMAProcess[2, {3/4}, {}, {4, {1/3}, {}}, 2], {0, 10^3}]]

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

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X tsm = TimeSeriesModelFit[data]

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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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X tsm["ParameterTable"]

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

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X ListPlot[PartialCorrelationFunction[data, {10}], Filling -> Axis, FillingStyle -> Thick, PlotStyle -> PointSize[Large], PlotTheme -> "VibrantColors", PlotRange -> {-1/3, 1}, AxesOrigin -> {0, 0}]

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

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X tsmSeasonal = TimeSeriesModelFit[data, {"SARMA", 4}]

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Compare with fitting longer autoregressive models.

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X tsmARlong = TimeSeriesModelFit[data, {"AR", 1 ;; 20}]

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

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X TableForm[ Outer[Compose, {tsm, tsmARlong, tsmSeasonal}, {"BIC", "AIC"}], TableHeadings -> {{"AR", "AR long", Subscript["SARMA", 4]}, {"BIC", "AIC"}}]

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