Common cycles in seasonal non-stationary time series

This paper extends the notion of common cycles to quarterly time series hav ing unit roots both at the zero and seasonal frequencies. It is shown that common cycles are present in the Hylleberg-Engle-Granger-Yoo decomposition of these series when there exists a linear combination of their seasonal di fferences which follows an MA process of order, at most, three. The pitfall s of seasonal adjustment for common cycles analysis are also documented. In ference on common cycles in seasonally cointegrated series is derived from existing statistical methods for codependence. Concepts and methods are ill ustrated with an empirical analysis of the comovements between consumption and output using Italian data. Copyright (C) 1999 John Wiley & Sons, Ltd.