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Markov-Switching Model Selection Using Kullback-Leibler Divergence

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Author Info
Smith, Aaron
Naik, Prasad A.
Tsai, Chih-Ling

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Abstract

In Markov-switching regression models, we use Kullback-Leibler (KL) divergence between the true and candidate models to select the number of states and variables simultaneously. In applying Akaike information criterion (AIC), which is an estimate of KL divergence, we find that AIC retains too many states and variables in the model. Hence, we derive a new information criterion, Markov switching criterion (MSC), which yields a marked improvement in state determination and variable selection because it imposes an appropriate penalty to mitigate the over-retention of states in the Markov chain. MSC performs well in Monte Carlo studies with single and multiple states, small and large samples, and low and high noise. Furthermore, it not only applies to Markov-switching regression models, but also performs well in Markov- switching autoregression models. Finally, the usefulness of MSC is illustrated via applications to the U.S. business cycle and the effectiveness of media advertising.

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Paper provided by University of California, Davis, Department of Agricultural and Resource Economics in its series Working Papers with number 11976.

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Date of creation: 2005
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Handle: RePEc:ags:ucdavw:11976

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Keywords: Research Methods/ Statistical Methods;

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  3. Hansen, Bruce E, 1992. "The Likelihood Ratio Test under Nonstandard Conditions: Testing the Markov Switching Model of GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages S61-82, Suppl. De. [Downloadable!] (restricted)
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  5. 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 357-84, March. [Downloadable!] (restricted)
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  7. Garcia, Rene, 1998. "Asymptotic Null Distribution of the Likelihood Ratio Test in Markov Switching Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(3), pages 763-88, August.
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  8. Kim, Chang-Jin, 1994. "Dynamic linear models with Markov-switching," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 1-22. [Downloadable!] (restricted)
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  14. Allan Timmermann, 2001. "Structural Breaks, Incomplete Information and Stock Prices," University of California at San Diego, Economics Working Paper Series 2001-02, Department of Economics, UC San Diego. [Downloadable!]
  15. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333. [Downloadable!] (restricted)
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  16. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70. [Downloadable!] (restricted)
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  1. José Casals Carro & Miguel Jerez Méndez & Sonia Sotoca López, 2006. "Decomposition of state-space Model with inputs: The theory and an application to estimate the ROI of advertising," Documentos del Instituto Complutense de Análisis Económico 0602, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales. [Downloadable!]
  2. Philippe J. Deschamps, 2007. "Comparing smooth transition and Markov switching autoregressive models of US Unemployment," DQE Working Papers 7, Department of Quantitative Economics, University of Freiburg/Fribourg Switzerland, revised 04 Jun 2008. [Downloadable!]
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