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Determining The Number Of Regimes In Markov Switching Var And Vma Models

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  • Maddalena Cavicchioli

Abstract

type="main" xml:id="jtsa12057-abs-0001"> We give stable finite-order vector autoregressive moving average (p-super- ,q-super- ) representations for M-state Markov switching second-order stationary time series whose autocovariances satisfy a certain matrix relation. The upper bounds for p-super- and q-super- are elementary functions of the dimension K of the process, the number M of regimes, the autoregressive and moving-average orders of the initial model. If there is no cancellation, the bounds become equalities, and this solves the identification problem. Our classes of time series include every M-state Markov switching multi-variate moving-average models and autoregressive models in which the regime variable is uncorrelated with the observable. Our results include, as particular cases, those obtained by Krolzig (1997) and improve the bounds given by Zhang and Stine (2001) and Francq and Zakoïan (2001) for our classes of dynamic models. A Monte Carlo experiment and an application on foreign exchange rates complete the article. Copyright © 2013 John Wiley & Sons, Ltd.

Suggested Citation

  • Maddalena Cavicchioli, 2014. "Determining The Number Of Regimes In Markov Switching Var And Vma Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(2), pages 173-186, March.
    • Handle: RePEc:bla:jtsera:v:35:y:2014:i:2:p:173-186
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    File URL: http://hdl.handle.net/10.1002/jtsa.12057
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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. 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.
    3. Cavicchioli, Maddalena, 2023. "Impulse response function analysis for Markov switching var models," Economics Letters, Elsevier, vol. 232(C).
    4. Marçal, Emerson & Simões, Oscar Rodrigues, 2024. "Current account and real effective exchange rate dynamics: the role of non-linear dynamics in Brazil," Textos para discussão 571, FGV EESP - Escola de Economia de São Paulo, Fundação Getulio Vargas (Brazil).
    5. Chuffart Thomas & Flachaire Emmanuel & Péguin-Feissolle Anne, 2018. "Testing for misspecification in the short-run component of GARCH-type models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(5), pages 1-17, December.
    6. 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).
    7. Maddalena Cavicchioli, 2020. "Invertibility and VAR Representations of Time-Varying Dynamic Stochastic General Equilibrium Models," Computational Economics, Springer;Society for Computational Economics, vol. 55(1), pages 61-86, January.
    8. Marie-Christine Duker & David S. Matteson & Ruey S. Tsay & Ines Wilms, 2024. "Vector AutoRegressive Moving Average Models: A Review," Papers 2406.19702, arXiv.org.
    9. Fiorentini, Gabriele & Planas, Christophe & Rossi, Alessandro, 2016. "Skewness and kurtosis of multivariate Markov-switching processes," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 153-159.
    10. Maddalena Cavicchioli, 2016. "Weak VARMA representations of regime-switching state-space models," Statistical Papers, Springer, vol. 57(3), pages 705-720, September.
    11. 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.
    12. Ahmed Ghezal & Maddalena Cavicchioli & Imane Zemmouri, 2024. "On the existence of stationary threshold bilinear processes," Statistical Papers, Springer, vol. 65(6), pages 3739-3767, August.

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