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The Spectral Representation of Markov-Switching Arma Models

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  • Beatrice Pataracchia

Abstract

In this paper we propose a method to derive the spectral representation in the case of a particular class of nonlinear models: Markov Switching ARMA models. The procedure simply relies on the application of the Riesz-Fisher Theorem which describes the spectral density as the Fourier transform of the autocovariance functions. We explicitly show the analytical structure of the spectral density in the simple Markov Switching AR(1). Finally, a monetary policy application of a Markov Switching VAR(4) is presented

Suggested Citation

  • Beatrice Pataracchia, 2008. "The Spectral Representation of Markov-Switching Arma Models," Department of Economics University of Siena 528, Department of Economics, University of Siena.
    • Handle: RePEc:usi:wpaper:528
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    Cited by:

    1. 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).
    2. Beatrice Pataracchia, 2008. "Design Limits in Regime-Switching Cases," Department of Economics University of Siena 529, Department of Economics, University of Siena.
    3. Chikashi Tsuji, 2014. "Did the Stock Market Regime Change after the Inauguration of the New Cabinet in Japan?," Business and Management Horizons, Macrothink Institute, vol. 2(1), pages 98-108, June.
    4. 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.
    5. Cavicchioli, Maddalena, 2013. "Spectral density of Markov-switching VARMA models," Economics Letters, Elsevier, vol. 121(2), pages 218-220.

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    More about this item

    Keywords

    Multivariate ARMA models; Regime-switching models; Markov switching models; Frequency Domain;
    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
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

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