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Complex Unit Roots And Business Cycles: Are They Real?

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Author Info
Bierens, Herman J.

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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.

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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 17 (2001)
Issue (Month): 05 (October)
Pages: 962-983
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Handle: RePEc:cup:etheor:v:17:y:2001:i:05:p:962-983_17

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  1. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2005. "Testing For Deterministic And Stochastic Cycles In Macroeconomic Time Series," Economics and Finance Discussion Papers 05-11, Economics and Finance Section, School of Social Sciences, Brunel University. [Downloadable!]
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  2. Morten Oe. Nielsen, . "Efficient Likelihold Inference in Nonstationary Univariate Models," Economics Working Papers 2001-8, School of Economics and Management, University of Aarhus. [Downloadable!]
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  3. Haitham A. Al Zoubi & Aktham Maghyereh, 2005. "Examining complex unit roots in the MENA countries industrial production indices," Applied Economics Letters, Taylor and Francis Journals, vol. 12(4), pages 255-259, March. [Downloadable!] (restricted)
  4. Fabio Busetti & Andrew Harvey, 2007. "Testing for trend," Temi di discussione (Economic working papers) 614, Bank of Italy, Economic Research Department. [Downloadable!]
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  5. Javier De Peña & Luis A. Gil-Alana, 2003. "Testing of Nonstationary Cycles in Financial Time Series Data," Faculty Working Papers 15/03, School of Economics and Business Administration, University of Navarra. [Downloadable!]
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  6. Jakob Roland Munch & Michael Svarer, . "Mortality and Socio-economic Differences in a Competing Risks Model," Economics Working Papers 2001-1, School of Economics and Management, University of Aarhus. [Downloadable!]
  7. Ignacio Rodríguez Carreño & L. Gila Useros, A. Malanda Trigueros, J. Navallas Irujo, J. Rodríguez Falces, S. Gómez Elvira, 2008. "Influence of Baseline Fluctuation Cancellation on Automatic Measurement of Motor Unit Action Potential Duration," Faculty Working Papers 13/08, School of Economics and Business Administration, University of Navarra. [Downloadable!]
  8. Urban, Dieter M., 2007. "Terms of Trade, Catch-up, and Home Market Effect: The Example of Japan," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
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  9. Guglielmo Maria Caporale & Juncal Cunado & Luis A. Gil-Alana, 2008. "Modelling Long-Run Trends and Cycles in Financial Time Series Data," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
  10. Luis A. Gil-Alana, 2004. "Unit root cycles in the US unemployment rate," Economics Bulletin, Economics Bulletin, vol. 3(7), pages 1-10. [Downloadable!]
  11. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2007. "Long Run and Cyclical Dynamics in the US Stock Market," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
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