Journal of Time Series Analysis

A NOTE ON TESTING FOR SEASONAL COINTEGRATION USING PRINCIPAL COMPONENTS IN THE FREQUENCY DOMAIN

Journal Article

Abstract. This paper deals with testing for cointegration at any frequency with a focus on the bounds tests proposed by Joyeux (Tests for seasonal cointegration using principal components. J. Time Ser. Anal. 13 (1992), 109–18). It is shown that this class of tests has asymptotic size equal to one because the author does not take into account non‐contemporaneous cointegration at frequencies other than zero and π. The consequences of this size distortion with finite samples are investigated by a Monte Carlo experiment. Bounds tests for contemporaneous cointegration are also proposed. Finally, an empirical example of testing for seasonal cointegration in monthly time series is presented and discussed.

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