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Some Properties Of Vector Autoregressive Processes With Markov-Switching Coefficients

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  • Yang, Minxian

Abstract

Some statistical properties of a vector autoregressive process with Markov-switching coefficients are considered. Sufficient conditions for this nonlinear process to be covariance stationary are given. The second moments of the process are derived under the conditions. The autocovariance matrix decays at exponential rate, permitting the application of the law of large numbers. Under the stationarity conditions, although sharing the “mean-reverting” property with conventional linear stationary processes, the process offers richer short-run dynamics such as conditional heteroskedasticity, asymmetric responses, and occasional nonstationary behavior.

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  • Yang, Minxian, 2000. "Some Properties Of Vector Autoregressive Processes With Markov-Switching Coefficients," Econometric Theory, Cambridge University Press, vol. 16(1), pages 23-43, February.
    • Handle: RePEc:cup:etheor:v:16:y:2000:i:01:p:23-43_16
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    1. Cavicchioli, Maddalena, 2017. "Asymptotic Fisher information matrix of Markov switching VARMA models," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 124-135.
    2. Luc Bauwens & Arie Preminger & Jeroen V. K. Rombouts, 2010. "Theory and inference for a Markov switching GARCH model," Econometrics Journal, Royal Economic Society, vol. 13(2), pages 218-244, July.
    3. 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.
    4. Adnan Haider & Musleh ud Din & Ejaz Ghani, 2011. "Consequences of Political Instability, Governance and Bureaucratic Corruption on Inflation and Growth: The Case of Pakistan," The Pakistan Development Review, Pakistan Institute of Development Economics, vol. 50(4), pages 773-807.
    5. Bibi, Abdelouahab & Ghezal, Ahmed, 2015. "Consistency of quasi-maximum likelihood estimator for Markov-switching bilinear time series models," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 192-202.
    6. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    7. Beg, A.B.M. Rabiul Alam & Anwar, Sajid, 2012. "Sources of volatility persistence: A case study of the U.K. pound/U.S. dollar exchange rate returns," The North American Journal of Economics and Finance, Elsevier, vol. 23(2), pages 165-184.
    8. 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.
    9. Francq, C. & Zakoian, J. -M., 2001. "Stationarity of multivariate Markov-switching ARMA models," Journal of Econometrics, Elsevier, vol. 102(2), pages 339-364, June.
    10. Nebojša Malešević & Dimitrije Marković & Gunter Kanitz & Marco Controzzi & Christian Cipriani & Christian Antfolk, 2018. "Vector Autoregressive Hierarchical Hidden Markov Models for Extracting Finger Movements Using Multichannel Surface EMG Signals," Complexity, Hindawi, vol. 2018, pages 1-12, February.
    11. Bildirici, Melike & Ersin, Özgür, 2012. "Nonlinear volatility models in economics: smooth transition and neural network augmented GARCH, APGARCH, FIGARCH and FIAPGARCH models," MPRA Paper 40330, University Library of Munich, Germany, revised May 2012.
    12. Sajjad Rasoul & Coakley Jerry & Nankervis John C, 2008. "Markov-Switching GARCH Modelling of Value-at-Risk," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(3), pages 1-31, September.
    13. 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.
    14. Hamilton, J.D., 2016. "Macroeconomic Regimes and Regime Shifts," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 163-201, Elsevier.
    15. Sofia Ruiz-Suarez & Vianey Leos-Barajas & Juan Manuel Morales, 2022. "Hidden Markov and Semi-Markov Models When and Why are These Models Useful for Classifying States in Time Series Data?," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 339-363, June.
    16. Stavros Degiannakis & Christos Floros & Enrique Salvador & Dimitrios Vougas, 2022. "On the stationarity of futures hedge ratios," Operational Research, Springer, vol. 22(3), pages 2281-2303, July.
    17. Maddalena Cavicchioli, 2021. "OLS Estimation of Markov switching VAR models: asymptotics and application to energy use," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 431-449, September.
    18. Kole, Erik & van Dijk, Dick, 2023. "Moments, shocks and spillovers in Markov-switching VAR models," Journal of Econometrics, Elsevier, vol. 236(2).
    19. Cavicchioli, Maddalena, 2023. "Statistical analysis of Markov switching vector autoregression models with endogenous explanatory variables," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    20. Aivazian, Sergey & Bereznyatskiy, Alexander & Brodsky, Boris & Darkhovsky, Boris, 2015. "Statistical analysis of variable-structure models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 84-105.
    21. Maddalena Cavicchioli, 2020. "A note on the asymptotic and exact Fisher information matrices of a Markov switching VARMA process," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 129-139, March.
    22. Degras, David & Ting, Chee-Ming & Ombao, Hernando, 2022. "Markov-switching state-space models with applications to neuroimaging," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    23. Dominique Guegan & Zhiping Lu, 2007. "A note on self-similarity for discrete time series," Post-Print halshs-00187910, HAL.

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