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Weak VARMA representations of regime-switching state-space models

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  • Maddalena Cavicchioli

    (Department of Economics “Marco Biagi”)

Abstract

We consider state-space representation of a multivariate dynamic process with Markov switching in both measurement and transition equations. Under appropriate moment conditions, we show that the autocovariance structure of such a process coincides with that of a stable VARMA model. This is potentially useful for statistical applications and for model selection as, for example, the identification of the regime number. Applications for classical Markov switching models and some numerical illustrations complete the paper.

Suggested Citation

  • Maddalena Cavicchioli, 2016. "Weak VARMA representations of regime-switching state-space models," Statistical Papers, Springer, vol. 57(3), pages 705-720, September.
    • Handle: RePEc:spr:stpapr:v:57:y:2016:i:3:d:10.1007_s00362-015-0675-1
    DOI: 10.1007/s00362-015-0675-1
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    References listed on IDEAS

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    1. Gourieroux,Christian & Monfort,Alain, 1997. "Time Series and Dynamic Models," Cambridge Books, Cambridge University Press, number 9780521423083.
    2. 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.
    3. Magnus, Jan R. & Neudecker, H., 1986. "Symmetry, 0-1 Matrices and Jacobians: A Review," Econometric Theory, Cambridge University Press, vol. 2(2), pages 157-190, August.
    4. Giordani, Paolo & Kohn, Robert & van Dijk, Dick, 2007. "A unified approach to nonlinearity, structural change, and outliers," Journal of Econometrics, Elsevier, vol. 137(1), pages 112-133, March.
    5. Kosei Fukuda, 2007. "Simulated real-time detection of multiple structural changes: Evidence from Japanese economic growth," Statistical Papers, Springer, vol. 48(4), pages 559-580, October.
    6. 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.
    7. Francq, C. & Zakoian, J. -M., 2001. "Stationarity of multivariate Markov-switching ARMA models," Journal of Econometrics, Elsevier, vol. 102(2), pages 339-364, June.
    8. Kim, Chang-Jin, 1994. "Dynamic linear models with Markov-switching," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 1-22.
    9. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    10. M. Salau, 2003. "The effects of different choices of order for autoregressive approximation on the Gaussian likelihood estimates for ARMA models," Statistical Papers, Springer, vol. 44(1), pages 89-105, January.
    11. M. Kharrati-Kopaei & A. Nematollahi & Z. Shishebor, 2009. "On the sufficient statistics for multivariate ARMA models: approximate approach," Statistical Papers, Springer, vol. 50(2), pages 261-276, March.
    12. Chang-Jin Kim & Charles R. Nelson, 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262112388, April.
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    Cited by:

    1. Maddalena Cavicchioli, 2016. "Statistical Analysis Of Mixture Vector Autoregressive Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 1192-1213, December.
    2. Marie-Christine Duker & David S. Matteson & Ruey S. Tsay & Ines Wilms, 2024. "Vector AutoRegressive Moving Average Models: A Review," Papers 2406.19702, arXiv.org.
    3. Abdoulkarim Ilmi Amir & Yacouba Boubacar Maïnassara, 2020. "Multivariate portmanteau tests for weak multiplicative seasonal VARMA models," Statistical Papers, Springer, vol. 61(6), pages 2529-2560, December.
    4. 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.
    5. Pierri Damian, 2024. "Accuracy in Recursive Minimal State Space Methods," Computational Economics, Springer;Society for Computational Economics, vol. 64(1), pages 263-305, July.
    6. 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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