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�Markov Switching Models for Volatility: Filtering, Approximation and Duality�

Author

Listed:
  • Monica Billio

    (Department of Economics, University Of Venice C� Foscari, Italy)

  • Maddalena Cavicchioli

    (Department of Economics, University Of Venice C� Foscari, Italy)

Abstract

This paper is devoted to show duality in the estimation of Markov Switching (MS) processes for volatility. It is well-known that MS-GARCH models suffer of path dependence which makes the estimation step unfeasible with usual Maximum Likelihood procedure. However, by rewriting the MS-GARCH model in a suitable linear State Space representation, we are able to give a unique framework to reconcile the estimation obtained by the Kalman Filter and with some auxiliary models proposed in the literature. Reasoning in the same way, we present a linear Filter for MS-Stochastic Volatility (MS-SV) models on which different conditioning sets yield more flexibility in the estimation. Estimation on simulated data and on short-term interest rates shows the feasibility of the proposed approach.

Suggested Citation

  • Monica Billio & Maddalena Cavicchioli, 2013. "�Markov Switching Models for Volatility: Filtering, Approximation and Duality�," Working Papers 2013:24, Department of Economics, University of Venice "Ca' Foscari".
    • Handle: RePEc:ven:wpaper:2013:24
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    References listed on IDEAS

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    1. Carvalho, Carlos M. & Lopes, Hedibert F., 2007. "Simulation-based sequential analysis of Markov switching stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4526-4542, May.
    2. Bauwens, Luc & Dufays, Arnaud & Rombouts, Jeroen V.K., 2014. "Marginal likelihood for Markov-switching and change-point GARCH models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 508-522.
    3. Gourieroux,Christian & Monfort,Alain, 1997. "Time Series and Dynamic Models," Cambridge Books, Cambridge University Press, number 9780521423083.
    4. Luc Bauwens & Arie Preminger & Jeroen V. K. Rombouts, 2010. "Theory and inference for a Markov switching GARCH model," Econometrics Journal, Royal Economic Society, vol. 13(2), pages 218-244, July.
    5. Jan Henneke & Svetlozar Rachev & Frank Fabozzi & Metodi Nikolov, 2011. "MCMC-based estimation of Markov Switching ARMA-GARCH models," Applied Economics, Taylor & Francis Journals, vol. 43(3), pages 259-271.
    6. Franc Klaassen, 2002. "Improving GARCH volatility forecasts with regime-switching GARCH," Empirical Economics, Springer, vol. 27(2), pages 363-394.
    7. Dueker, Michael J, 1997. "Markov Switching in GARCH Processes and Mean-Reverting Stock-Market Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 26-34, January.
    8. Monica Billio & Massimiliano Caporin, 2005. "Multivariate Markov switching dynamic conditional correlation GARCH representations for contagion analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(2), pages 145-161, November.
    9. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(4), pages 493-530.
    10. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    11. Billio, Monica & Casarin, Roberto & Osuntuyi, Anthony, 2016. "Efficient Gibbs sampling for Markov switching GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 37-57.
    12. Lamoureux, Christopher G & Lastrapes, William D, 1990. "Persistence in Variance, Structural Change, and the GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 225-234, April.
    13. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    14. So, Mike K P & Lam, K & Li, W K, 1998. "A Stochastic Volatility Model with Markov Switching," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 244-253, April.
    15. Pelletier, Denis, 2006. "Regime switching for dynamic correlations," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 445-473.
    16. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 247-264.
    17. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    18. Christian Francq & Jean‐Michel Zakoïan, 2012. "Strict Stationarity Testing and Estimation of Explosive and Stationary Generalized Autoregressive Conditional Heteroscedasticity Models," Econometrica, Econometric Society, vol. 80(2), pages 821-861, March.
    19. Kim, Chang-Jin, 1994. "Dynamic linear models with Markov-switching," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 1-22.
    20. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
    21. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
    22. Chang-Jin Kim & Charles R. Nelson, 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262112388, April.
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    More about this item

    Keywords

    Markov Switching; MS-GARCH model; MS-SV model; estimation; auxiliary model; Kalman Filter.;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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