Common cycles in seasonal non-stationary time series
将共同周期概念扩展到具有零频和季节频率单位根的季度时间序列，证明当季节差分的线性组合服从至多三阶移动平均过程时存在共同周期，并用意大利数据分析了消费与产出的协同波动。
This paper extends the notion of common cycles to quarterly time series having 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 differences which follows an MA process of order, at most, three. The pitfalls of seasonal adjustment for common cycles analysis are also documented. Inference on common cycles in seasonally cointegrated series is derived from existing statistical methods for codependence. Concepts and methods are illustrated with an empirical analysis of the comovements between consumption and output using Italian data. Copyright © 1999 John Wiley & Sons, Ltd.