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COMPLEX UNIT ROOTS AND BUSINESS CYCLES: ARE THEY REAL?

Published online by Cambridge University Press:  25 September 2001

Herman J. Bierens
Herman J. Bierens
Affiliation:
Pennsylvania State University and Tilburg University
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Abstract

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.

Type
Research Article
Information
Econometric Theory , Volume 17 , Issue 5 , October 2001 , pp. 962 - 983
Copyright
© 2001 Cambridge University Press

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