Cointegration for Seasonal Time Series Processes

This paper examines types of cointegration for bivariate seasonal time series, namely seasonal cointegration, periodic cointegration and nonperiodic cointegration. The admissable form(s) for any cointegration is shown to depend crucially on the univariate unit root properties of the series. When both processes are (conventionally) integrated, only nonperiodic cointegration is possible. Periodically integrated processes can be nonperiodically or periodically cointegrated, with the cointegrating coefficients related to the periodic integration coefficients of the separate variables. The richest set of possibilities emerge when both series are seasonally integrated, since all three types of cointegration can then apply. Periodic and seasonal cointegration are shown to imply distinct restrictions, with nonperiodic integration a special case of seasonal integration. The case of partial cointegration is also considered, whereby stationary linear combinations apply to only some of the unit roots present in the univariate processes. JEL classifications: C22, C32, C51