In this paper a model selection test procedure for seasonal time series is proposed. It uses the estimated autocorrelations of the moving average part of the Box and Jenkins airline model. This ensures that the test statistics asymptotically follow standard normal distributions. The merits and limitations of the procedure are illustrated via simulations as well as by some empirical series.

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Journal Statistics & Probability Letters
Franses, Ph.H.B.F. (1993). A model selection procedure for time series with seasonality. Statistics & Probability Letters, 253–258. doi:10.1016/0167-7152(93)90128-6