IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v17y2001i05p962-983_17.html
   My bibliography  Save this article

Complex Unit Roots And Business Cycles: Are They Real?

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0266466601175055/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. del Barrio Castro, Tomás & Rachinger, Heiko, 2021. "Aggregation of Seasonal Long-Memory Processes," Econometrics and Statistics, Elsevier, vol. 17(C), pages 95-106.
    2. del Barrio Castro, Tomás & Osborn, Denise R., 2023. "Periodic Integration and Seasonal Unit Roots," MPRA Paper 117935, University Library of Munich, Germany, revised 2023.
    3. Tomás del Barrio Castro & Gianluca Cubadda & Denise R. Osborn, 2022. "On cointegration for processes integrated at different frequencies," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 412-435, May.
    4. del Barrio Castro, Tomás & Rodrigues, Paulo M.M. & Robert Taylor, A.M., 2018. "Semi-Parametric Seasonal Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 34(2), pages 447-476, April.
    5. Castro, Tomás del Barrio & Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2013. "The Impact Of Persistent Cycles On Zero Frequency Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 29(6), pages 1289-1313, December.
    6. Chambers, Marcus J. & Ercolani, Joanne S. & Taylor, A.M. Robert, 2014. "Testing for seasonal unit roots by frequency domain regression," Journal of Econometrics, Elsevier, vol. 178(P2), pages 243-258.
    7. Mr. Thomas Helbling & Mr. Tamim Bayoumi, 2003. "Are they All in the Same Boat? the 2000-2001 Growth Slowdown and the G-7 Business Cycle Linkages," IMF Working Papers 2003/046, International Monetary Fund.
    8. Dagum, Estela Bee, 2010. "Business Cycles and Current Economic Analysis/Los ciclos económicos y el análisis económico actual," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 28, pages 577-594, Diciembre.
    9. Natasha Kang, Da & Marmer, Vadim, 2024. "Modeling long cycles," Journal of Econometrics, Elsevier, vol. 242(1).
    10. Mercè Sala-Rios & Teresa Torres-Solé & Mariona Farré-Perdiguer, 2016. "Credit and business cycles’ relationship: evidence from Spain," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 15(3), pages 149-171, December.
    11. Adrian Penalver & Daniele Siena, 2021. "The Deflationary Bias of the ZLB and the FED’s Strategic Response," Working papers 843, Banque de France.
    12. Viv B. Hall & C. John McDermott, 2007. "Regional business cycles in New Zealand: Do they exist? What might drive them?," Papers in Regional Science, Wiley Blackwell, vol. 86(2), pages 167-191, June.
    13. Vincent, BODART & Konstantin, KHOLODILIN & Fati, SHADMAN-MEHTA, 2005. "Identifying and Forecasting the Turning Points of the Belgian Business Cycle with Regime-Switching and Logit Models," Discussion Papers (ECON - Département des Sciences Economiques) 2005006, Université catholique de Louvain, Département des Sciences Economiques.
    14. Minakshy Iyer, 2006. "An Index of Uncertainty for Business Cycle Leading Indicators," Working Papers id:751, eSocialSciences.
    15. Tomás Barrio Castro & Andrii Bodnar & Andreu Sansó, 2017. "Numerical distribution functions for seasonal unit root tests with OLS and GLS detrending," Computational Statistics, Springer, vol. 32(4), pages 1533-1568, December.
    16. Mercè Sala-Rios & Teresa Torres-Solé & Mariona Farré-Perdiguer, 2018. "Immigrants’ employment and the business cycle in Spain: taking account of gender and origin," Economia Politica: Journal of Analytical and Institutional Economics, Springer;Fondazione Edison, vol. 35(2), pages 463-490, August.
    17. F. DePenya & L. Gil-Alana, 2006. "Testing of nonstationary cycles in financial time series data," Review of Quantitative Finance and Accounting, Springer, vol. 27(1), pages 47-65, August.
    18. Matteo Barigozzi & Marco Lippi & Matteo Luciani, 2020. "Cointegration and Error Correction Mechanisms for Singular Stochastic Vectors," Econometrics, MDPI, vol. 8(1), pages 1-23, February.
    19. Rodrigues, Paulo M. M. & Taylor, A. M. Robert, 2004. "Alternative estimators and unit root tests for seasonal autoregressive processes," Journal of Econometrics, Elsevier, vol. 120(1), pages 35-73, May.
    20. Kim, Chang-Jin & Nelson, Charles R, 2001. "A Bayesian Approach to Testing for Markov-Switching in Univariate and Dynamic Factor Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(4), pages 989-1013, November.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:17:y:2001:i:05:p:962-983_17. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/ect .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.