COMPLEX UNIT ROOTS AND BUSINESS CYCLES: ARE THEY REAL?
研究了自回归滑动平均过程中复共轭单位根的渐近性质，提出一种非参数检验方法，并应用于美国月度失业人数年变化数据，检验商业周期频率中是否存在复单位根。
In this paper the asymptotic properties of ARMA processes with complex-conjugate unit roots in the AR lag polynomial are studied. These processes behave quite differently from regular unit root processes (with a single root equal to one). In particular, the asymptotic properties of a standardized version of the periodogram for such processes are analyzed, and a nonparametric test of the complex unit root hypothesis against the stationarity hypothesis is derived. This test is applied to the annual change of the monthly number of unemployed in the United States to see whether this time series has complex unit roots in the business cycle frequencies.