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Multivariate Time Series With Various Hidden Unit Roots, Part I

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  • Gregoir, Stéphane

Abstract

Following the approach proposed by Gregoir and Laroque (1993, Econometric Theory 9, 329–342), we consider a class of multivariate processes that, when differenced enough, yields covariance stationary processes whose determinant of the matrix series associated with their Wold representation has various unit roots with various orders of multiplicity we restrict to be integers. A representation theorem is provided that involves different polynomial error correction terms at each frequency associated with each unit root. An identification criterion for each set of error correction terms is proposed.

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  • 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.
    • Handle: RePEc:cup:etheor:v:15:y:1999:i:04:p:435-468_15
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    Cited by:

    1. Martin Wagner, 2010. "Cointegration analysis with state space models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(3), pages 273-305, September.
    2. 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.
    3. 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.
    4. del Barrio Castro, Tomás & Rachinger, Heiko, 2021. "Aggregation of Seasonal Long-Memory Processes," Econometrics and Statistics, Elsevier, vol. 17(C), pages 95-106.
    5. 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.
    6. Guglielmo Maria Caporale & Luis Gil‐Alana, 2014. "Long‐Run and Cyclical Dynamics in the US Stock Market," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(2), pages 147-161, March.
    7. 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.
    8. Fabio Busetti, 2006. "Tests of seasonal integration and cointegration in multivariate unobserved component models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 419-438.
    9. Guglielmo Caporale & Luis Gil-Alana, 2007. "Testing for deterministic and stochastic cycles in macroeconomic time series," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 34(2), pages 155-169, April.
    10. Dietmar Bauer & Martin Wagner, 2002. "A Canonical Form for Unit Root Processes in the State Space Framework," Diskussionsschriften dp0204, Universitaet Bern, Departement Volkswirtschaft.
    11. Dietmar Bauer & Martin Wagner, 2002. "Asymptotic Properties of Pseudo Maximum Likelihood Estimates for Multiple Frequency I(1) Processes," Diskussionsschriften dp0205, Universitaet Bern, Departement Volkswirtschaft.
    12. Massimo Franchi & Paolo Paruolo, 2021. "Cointegration, Root Functions and Minimal Bases," Econometrics, MDPI, vol. 9(3), pages 1-27, August.
    13. 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.
    14. El Montasser, Ghassen & Boufateh, Talel & Issaoui, Fakhri, 2013. "The seasonal KPSS test when neglecting seasonal dummies: a Monte Carlo analysis," MPRA Paper 46226, University Library of Munich, Germany.
    15. Lacroix, R., 1999. "Testing for Zeros in the Spectrum of an Univariate Stationary Process: Part I," Working papers 70, Banque de France.
    16. Dietmar Bauer & Martin Wagner, 2003. "On Polynomial Cointegration in the State Space Framework," Diskussionsschriften dp0313, Universitaet Bern, Departement Volkswirtschaft.
    17. 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.
    18. 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.
    19. repec:ebl:ecbull:v:3:y:2004:i:7:p:1-10 is not listed on IDEAS
    20. L.A. Gil-Alanaa, 2007. "Testing The Existence of Multiple Cycles in Financial and Economic Time Series," Annals of Economics and Finance, Society for AEF, vol. 8(1), pages 1-20, May.
    21. Dorina Lazar & Michel Denuit, 2011. "New evidence for underwriting cycles in US property-liability insurance," Journal of Risk Finance, Emerald Group Publishing, vol. 13(1), pages 4-12, December.
    22. del Barrio Castro, Tomás & Osborn, Denise R., 2023. "Periodic Integration and Seasonal Unit Roots," MPRA Paper 117935, University Library of Munich, Germany, revised 2023.

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