Groupe d’études et de recherche en analyse des décisions


On Consistent Testing for Serial Correlation in Seasonal Time Series Models

The author considers serial correlation testing in seasonal models. A test statistic is derived, using a spectral approach. Spectral tests usually rely on classical kernel-based spectral density estimators, with kernels assigning large (small) weights to low (high) order lags. Under seasonality, large autocorrelations may occur at seasonal lags, thus rendering the weighting scheme of classical kernel estimators inefficient. In view of this, the author proposes new test statistics, relying on Shin's (2004) spectral density estimator, whose weighting scheme harmonizes with the features of typical seasonal time series. He derives the distribution under the null hypothesis of the proposed test statistic and performs analyses under fixed and local alternatives. The consistency of the test is established under a general fixed alternative. The author makes recommendations for the choice of the smoothing parameters. His simulation results suggest that the new test statistics provide more powerful procedures against seasonality than do classical weighting schemes. An application with real monthly data is presented.

, 36 pages