Effects of misspecification of seasonal cointegrating ranks : an empirical study

We investigate the effects of the misspecification of cointegrating ranks at other frequencies on the inference of seasonal cointegration at the frequency of interest such as test for cointegrating rank and estimation of cointegrating vector. Earlier studies mostly focused on a single frequency corresponding to a seasonal root at a time, ignoring possible cointegration at the remaining frequencies. We investigate the effects of the misspecification, particularly in the case of finite samples by adopting Gaussian reduced rank estimation by Ahn and Reinsel (1994) that considered cointegration at all frequencies of seasonal unit roots simultaneously. It is observed that the identification of the seasonal cointegrating rank at the frequency of interest is robust to the over-specification of the cointegrating ranks at other frequencies, whereas it is very sensitive to underspecification.