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State space Markov switching models using wavelets

Author

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  • Alencar Airlane P.

    (Institute of Mathematics and Statistics, Statistics Department, University of São Paulo, Rua do Matão, 1010, 05508-090, São Paulo, SP, Brazil)

  • Morettin Pedro A.

    (Institute of Mathematics and Statistics, Statistics Department, University of São Paulo, Rua do Matão, 1010, 05508-090, São Paulo, SP, Brazil)

  • Toloi Clelia M.C.

    (Institute of Mathematics and Statistics, Statistics Department, University of São Paulo, Rua do Matão, 1010, 05508-090, São Paulo, SP, Brazil)

Abstract

We propose a state space model with Markov switching, whose regimes are associated with the model parameters and regime transition probabilities are modeled using wavelets. The estimation is based on the maximum likelihood method using the EM algorithm and a bootstrap method is proposed in order to assess the distribution of the maximum likelihood estimators. To evaluate the state variables and regime probabilities, the Kalman filter and a probability filter procedure conditional on each possible regime, at each instant, are used. These procedures are evaluated with simulated data and illustrated with the US monthly industrial production index from July 1968 to February 2011.

Suggested Citation

  • Alencar Airlane P. & Morettin Pedro A. & Toloi Clelia M.C., 2013. "State space Markov switching models using wavelets," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(2), pages 221-238, April.
    • Handle: RePEc:bpj:sndecm:v:17:y:2013:i:2:p:221-238:n:2
    DOI: 10.1515/snde-2012-0020
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    References listed on IDEAS

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    1. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, Decembrie.
    2. Gençay, Ramazan & Gençay, Ramazan & Selçuk, Faruk & Whitcher, Brandon J., 2001. "An Introduction to Wavelets and Other Filtering Methods in Finance and Economics," Elsevier Monographs, Elsevier, edition 1, number 9780122796708.
    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. Arthur F. Burns & Wesley C. Mitchell, 1946. "Measuring Business Cycles," NBER Books, National Bureau of Economic Research, Inc, number burn46-1, March.
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