Seasonality, nonstationarity and the forecasting of monthly time series

We focus on two forecasting models for a monthly time series. The first model requires that the variable is first order and seasonally differenced. The second model considers the series only in its first differences, while seasonality is modeled with a constant and seasonal dummies. A method to distinguish empirically between these two models is presented. The relevance of this method is established by simulation results as well as empirical evidence, which show, first, that conventional autocorrelation checks are often not discriminative and, second, that considering the first model while the second is more appropriate yields a deterioration of forecasting performance.

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