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Complex Unit Roots And Business Cycles: Are They Real?

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  • Bierens, Herman J.

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.

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  • Bierens, Herman J., 2001. "Complex Unit Roots And Business Cycles: Are They Real?," Econometric Theory, Cambridge University Press, vol. 17(5), pages 962-983, October.
    • Handle: RePEc:cup:etheor:v:17:y:2001:i:05:p:962-983_17
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    References listed on IDEAS

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    1. Francis X. Diebold & Glenn D. Rudebusch, 1999. "Business Cycles: Durations, Dynamics, and Forecasting," Economics Books, Princeton University Press, edition 1, number 6636.
    2. Gregoir, Stéphane, 1999. "Multivariate Time Series With Various Hidden Unit Roots, Part I," Econometric Theory, Cambridge University Press, vol. 15(4), pages 435-468, August.
    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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