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On Markov-Switching Arma Processes—Stationarity, Existence Of Moments, And Geometric Ergodicity

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  • Stelzer, Robert

Abstract

The probabilistic properties of ℝd-valued Markov-switching autoregressive moving average (ARMA) processes with a general state space parameter chain are analyzed. Stationarity and ergodicity conditions are given, and an easy-to-check general sufficient stationarity condition based on a tailor-made norm is introduced. Moreover, it is shown that causality of all individual regimes is neither a necessary nor a sufficient criterion for strict negativity of the associated Lyapunov exponent.Finiteness of moments is also considered and geometric ergodicity and strong mixing are proven. The easily verifiable sufficient stationarity condition is extended to ensure these properties.

Suggested Citation

  • Stelzer, Robert, 2009. "On Markov-Switching Arma Processes—Stationarity, Existence Of Moments, And Geometric Ergodicity," Econometric Theory, Cambridge University Press, vol. 25(1), pages 43-62, February.
    • Handle: RePEc:cup:etheor:v:25:y:2009:i:01:p:43-62_09
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    Cited by:

    1. Yacouba Boubacar Maïnassara & Landy Rabehasaina, 2020. "Estimation of weak ARMA models with regime changes," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 1-52, April.
    2. Francesco Giordano & Marcella Niglio & Cosimo Damiano Vitale, 2023. "Linear approximation of the Threshold AutoRegressive model: an application to order estimation," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 27-56, March.
    3. 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).
    4. Mélard, Guy, 2022. "An indirect proof for the asymptotic properties of VARMA model estimators," Econometrics and Statistics, Elsevier, vol. 21(C), pages 96-111.
    5. Francesco Giordano & Cira Perna & Cosimo Vitale, 2012. "A comment on “An analysis of global warming in the Alpine Region based on nonlinear nonstationary time series models” by F. Battaglia and M. K. Protopapas," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(3), pages 355-361, August.
    6. Marcella Niglio & Cosimo Damiano Vitale, 2012. "Local Unit Roots and Global Stationarity of TARMA Models," Methodology and Computing in Applied Probability, Springer, vol. 14(1), pages 17-34, March.
    7. Cavicchioli, Maddalena, 2023. "Impulse response function analysis for Markov switching var models," Economics Letters, Elsevier, vol. 232(C).
    8. 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.
    9. 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).
    10. Marie-Christine Duker & David S. Matteson & Ruey S. Tsay & Ines Wilms, 2024. "Vector AutoRegressive Moving Average Models: A Review," Papers 2406.19702, arXiv.org.
    11. João Nicolau & Paulo M. M. Rodrigues, 2019. "A New Regression-Based Tail Index Estimator," The Review of Economics and Statistics, MIT Press, vol. 101(4), pages 667-680, October.
    12. 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.
    13. Kole, Erik & van Dijk, Dick, 2023. "Moments, shocks and spillovers in Markov-switching VAR models," Journal of Econometrics, Elsevier, vol. 236(2).
    14. Cavicchioli, Maddalena, 2023. "Statistical analysis of Markov switching vector autoregression models with endogenous explanatory variables," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    15. Guy Melard, 2020. "An Indirect Proof for the Asymptotic Properties of VARMA Model Estimators," Working Papers ECARES 2020-10, ULB -- Universite Libre de Bruxelles.
    16. Lee, Oesook & Lee, Jungwha, 2014. "The functional central limit theorem for the multivariate MS–ARMA–GARCH model," Economics Letters, Elsevier, vol. 125(3), pages 331-335.
    17. Taamouti, Abderrahim, 2012. "Moments of multivariate regime switching with application to risk-return trade-off," Journal of Empirical Finance, Elsevier, vol. 19(2), pages 292-308.
    18. Cavicchioli, Maddalena, 2013. "Spectral density of Markov-switching VARMA models," Economics Letters, Elsevier, vol. 121(2), pages 218-220.

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