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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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    1. Noah Williams & Lars E.O. Svensson, 2005. "Monetary Policy with Model Uncertainty: Distribution Forecast Targeting," Computing in Economics and Finance 2005 108, Society for Computational Economics.
    2. 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.
    3. Glenn Rudebusch & Lars E.O. Svensson, 1999. "Policy Rules for Inflation Targeting," NBER Chapters, in: Monetary Policy Rules, pages 203-262, National Bureau of Economic Research, Inc.
    4. Francq, C. & Zakoian, J. -M., 2001. "Stationarity of multivariate Markov-switching ARMA models," Journal of Econometrics, Elsevier, vol. 102(2), pages 339-364, June.
    5. Brock, William A. & Durlauf, Steven N. & Nason, James M. & Rondina, Giacomo, 2007. "Simple versus optimal rules as guides to policy," Journal of Monetary Economics, Elsevier, vol. 54(5), pages 1372-1396, July.
    6. Mr. Ravi Balakrishnan & Mr. Sam Ouliaris, 2006. "U.S. Inflation Dynamics: What Drives Them Over Different Frequencies?," IMF Working Papers 2006/159, International Monetary Fund.
    7. Otrok, Christopher & Ravikumar, B. & Whiteman, Charles H., 2002. "Habit formation: a resolution of the equity premium puzzle?," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1261-1288, September.
    8. Brock, William A. & Durlauf, Steven N. & Rondina, Giacomo, 2013. "Design limits and dynamic policy analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2710-2728.
    9. Alexei Onatski & Noah Williams, 2003. "Modeling Model Uncertainty," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1087-1122, September.
    10. Otrok, Christopher, 2001. "Spectral Welfare Cost Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(2), pages 345-367, May.
    11. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
    12. William A. Brock & Steven N. Durlauf, 2004. "Elements of a Theory of Design Limits to Optimal Policy," Manchester School, University of Manchester, vol. 72(s1), pages 1-18, September.
    13. John B. Taylor, 1999. "Monetary Policy Rules," NBER Books, National Bureau of Economic Research, Inc, number tayl99-1.
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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. Cavicchioli, Maddalena, 2023. "Impulse response function analysis for Markov switching var models," Economics Letters, Elsevier, vol. 232(C).
    3. Beatrice Pataracchia, 2008. "Design Limits in Regime-Switching Cases," Department of Economics University of Siena 529, Department of Economics, University of Siena.
    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. 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.
    6. Cavicchioli, Maddalena, 2013. "Spectral density of Markov-switching VARMA models," Economics Letters, Elsevier, vol. 121(2), pages 218-220.
    7. 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).
    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.

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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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