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Autocovariance Structure of Markov Regime Switching Models and Model Selection

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  • Jing Zhang
  • Robert A. Stine

Abstract

We show that the covariance function of a second‐order stationary vector Markov regime switching time series has a vector ARMA(p,q) representation, where upper bounds for p and q are elementary functions of the number of regimes. These bounds apply to vector Markov regime switching processes with both mean–variance and autoregressive switching. This result yields an easily computed method for setting a lower bound on the number of underlying Markov regimes from an estimated autocovariance function.

Suggested Citation

  • Jing Zhang & Robert A. Stine, 2001. "Autocovariance Structure of Markov Regime Switching Models and Model Selection," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(1), pages 107-124, January.
    • Handle: RePEc:bla:jtsera:v:22:y:2001:i:1:p:107-124
    DOI: 10.1111/1467-9892.00214
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    Cited by:

    1. Cavicchioli, Maddalena, 2023. "Statistical analysis of Markov switching vector autoregression models with endogenous explanatory variables," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    2. D.S. Poskitt & Jing Zhang, 2004. "Estimating Components in Finite Mixtures and Hidden Markov Models," Monash Econometrics and Business Statistics Working Papers 10/04, Monash University, Department of Econometrics and Business Statistics.
    3. Maddalena Cavicchioli, 2014. "Autocovariance and Linear Transformations of Markov Switching VARMA Processes," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 6(4), pages 275-289, December.
    4. Cavicchioli, Maddalena, 2023. "Impulse response function analysis for Markov switching var models," Economics Letters, Elsevier, vol. 232(C).
    5. Huseyin Tastan & Nuri Yildirim, 2008. "Business cycle asymmetries in Turkey: an application of Markov-switching autoregressions," International Economic Journal, Taylor & Francis Journals, vol. 22(3), pages 315-333.
    6. Psaradakis, Zacharias, 2002. "On the asymptotic behaviour of unit-root tests in the presence of a Markov trend," Statistics & Probability Letters, Elsevier, vol. 57(1), pages 101-109, March.
    7. Johannes Hauptmann & Anja Hoppenkamps & Aleksey Min & Franz Ramsauer & Rudi Zagst, 2014. "Forecasting market turbulence using regime-switching models," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 28(2), pages 139-164, May.
    8. Maddalena Cavicchioli, 2013. "�Determining the Number of Regimes in Markov-Switching VAR and VMA Models�," Working Papers 2013:03, Department of Economics, University of Venice "Ca' Foscari".
    9. Altug, Sumru & Bildirici, Melike, 2010. "Business Cycles around the Globe: A Regime-switching Approach," CEPR Discussion Papers 7968, C.E.P.R. Discussion Papers.
    10. Zacharias Psaradakis & Nicola Spagnolo, 2003. "On The Determination Of The Number Of Regimes In Markov‐Switching Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(2), pages 237-252, March.
    11. Cavicchioli, Maddalena, 2024. "A matrix unified framework for deriving various impulse responses in Markov switching VAR: Evidence from oil and gas markets," The Journal of Economic Asymmetries, Elsevier, vol. 29(C).
    12. Maddalena Cavicchioli, 2015. "Likelihood Ratio Test and Information Criteria for Markov Switching Var Models: An Application to the Italian Macroeconomy," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 1(3), pages 315-332, November.
    13. Josh Stillwagon & Peter Sullivan, 2020. "Markov switching in exchange rate models: will more regimes help?," Empirical Economics, Springer, vol. 59(1), pages 413-436, July.
    14. Marie-Christine Duker & David S. Matteson & Ruey S. Tsay & Ines Wilms, 2024. "Vector AutoRegressive Moving Average Models: A Review," Papers 2406.19702, arXiv.org.
    15. Kole, Erik & van Dijk, Dick, 2023. "Moments, shocks and spillovers in Markov-switching VAR models," Journal of Econometrics, Elsevier, vol. 236(2).
    16. Francq, Christian & ZakoI¨an, Jean-Michel, 2005. "The L2-structures of standard and switching-regime GARCH models," Stochastic Processes and their Applications, Elsevier, vol. 115(9), pages 1557-1582, September.
    17. Maddalena Cavicchioli, 2016. "Weak VARMA representations of regime-switching state-space models," Statistical Papers, Springer, vol. 57(3), pages 705-720, September.
    18. Christian Glocker & Werner Hölzl, 2015. "Bestimmung einer Konjunkturampel für Österreich auf Basis des WIFO-Konjunkturtests," WIFO Monatsberichte (monthly reports), WIFO, vol. 88(3), pages 175-183, March.
    19. Nan Li & Simon S. Kwok, 2021. "Jointly determining the state dimension and lag order for Markov‐switching vector autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 471-491, July.
    20. Cavicchioli, Maddalena, 2013. "Spectral density of Markov-switching VARMA models," Economics Letters, Elsevier, vol. 121(2), pages 218-220.

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