Explain how to detect and adjust for seasonal effects in a time-series model, and work out and explain a forecast from an AR model that includes a seasonal lag
The idea
Seasonality shows up as a significant residual autocorrelation at the seasonal lag, four for quarterly data and twelve for monthly data, after an AR model is fitted. The correction is to add that lag as a regressor, for example x(t) = b0 + b1x(t − 1) + b2x(t − 4) + ε for quarterly data, then check the residual autocorrelations again. To forecast, plug in the latest value for the first lag and the value from the same season a year earlier for the seasonal lag. The common slip is miscounting the seasonal lag: four quarters before the first quarter of next year is the first quarter of this year.
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