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Spectral density of Markov-switching VARMA models

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  • Cavicchioli, Maddalena

Abstract

We review the main results of Francq and Zakoïan (2001) on stationarity and the autocovariance function for Markov-switching VARMA models. Then we derive a formula in closed form for the spectral density of such models, and describe some new properties of it. Our results improve those obtained by Pataracchia (2011) and complete some of Francq and Zakoïan (2001).

Suggested Citation

  • Cavicchioli, Maddalena, 2013. "Spectral density of Markov-switching VARMA models," Economics Letters, Elsevier, vol. 121(2), pages 218-220.
    • Handle: RePEc:eee:ecolet:v:121:y:2013:i:2:p:218-220
    DOI: 10.1016/j.econlet.2013.07.022
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    4. Pataracchia, Beatrice, 2011. "The spectral representation of Markov switching ARMA models," Economics Letters, Elsevier, vol. 112(1), pages 11-15, July.
    5. Francq, C. & Zakoian, J. -M., 2001. "Stationarity of multivariate Markov-switching ARMA models," Journal of Econometrics, Elsevier, vol. 102(2), pages 339-364, June.
    6. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
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    Citations

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    Cited by:

    1. 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).
    2. Elie Bouri & Imad Kachacha & Donald Lien & David Roubaud, 2017. "Short- and long-run causality across the implied volatility of crude oil and agricultural commodities," Economics Bulletin, AccessEcon, vol. 37(2).
    3. Cavicchioli, Maddalena, 2023. "Impulse response function analysis for Markov switching var models," Economics Letters, Elsevier, vol. 232(C).
    4. Marie-Christine Duker & David S. Matteson & Ruey S. Tsay & Ines Wilms, 2024. "Vector AutoRegressive Moving Average Models: A Review," Papers 2406.19702, arXiv.org.
    5. 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.
    6. Pierri Damian, 2024. "Accuracy in Recursive Minimal State Space Methods," Computational Economics, Springer;Society for Computational Economics, vol. 64(1), pages 263-305, July.
    7. Maria Chiara Pocelli & Manuel L. Esquível & Nadezhda P. Krasii, 2023. "Spectral Analysis for Comparing Bitcoin to Currencies and Assets," Mathematics, MDPI, vol. 11(8), pages 1-21, April.
    8. 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.
    9. Cavicchioli, Maddalena, 2023. "Statistical analysis of Markov switching vector autoregression models with endogenous explanatory variables," Journal of Multivariate Analysis, Elsevier, vol. 196(C).

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    More about this item

    Keywords

    Markov-switching VARMA; Spectral density; Stable VARMA representation;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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