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Complex Unit Roots and Business Cycles: Are They Real?

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  • Herman J. Bierens

    (Pennsylvania State University)

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 processes with a single root equal to 1. 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 US, in order to see whether this time series has complex unit roots in the business cycle frequencies.

Suggested Citation

  • Herman J. Bierens, 2000. "Complex Unit Roots and Business Cycles: Are They Real?," Econometric Society World Congress 2000 Contributed Papers 0197, Econometric Society.
    • Handle: RePEc:ecm:wc2000:0197
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    References listed on IDEAS

    as
    1. Gregoir, Stéphane, 1999. "Multivariate Time Series With Various Hidden Unit Roots, Part Ii," Econometric Theory, Cambridge University Press, vol. 15(4), pages 469-518, August.
    2. Francis X. Diebold & Glenn D. Rudebusch, 1999. "Business Cycles: Durations, Dynamics, and Forecasting," Economics Books, Princeton University Press, edition 1, number 6636.
    3. Gregoir, Stephane, 2006. "Efficient tests for the presence of a pair of complex conjugate unit roots in real time series," Journal of Econometrics, Elsevier, vol. 130(1), pages 45-100, January.
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