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The Spectral Representation of Markov-Switching Arma Models

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Author Info
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

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Paper provided by Department of Economics, University of Siena in its series Department of Economics University of Siena with number 528.

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Date of creation: Mar 2008
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Handle: RePEc:usi:wpaper:528

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Related research
Keywords: Multivariate ARMA models; Regime-switching models; Markov switching models; Frequency Domain;

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Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Statistical Decision Theory; Operations Research
E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

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  1. 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. [Downloadable!] (restricted)
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  2. 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.
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  3. Alexei Onatski & Noah Williams, 2003. "Modeling Model Uncertainty," NBER Working Papers 9566, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  4. 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, 09. [Downloadable!] (restricted)
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  5. 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. [Downloadable!]
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  6. 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 345-67, May.
  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. [Downloadable!] (restricted)
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