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Parameter estimation of an asset price model driven by a weak hidden Markov chain

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  • Xi, Xiaojing
  • Mamon, Rogemar
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    Abstract

    We introduce a weak hidden Markov model (WHMM) in an attempt to capture more accurately the evolution of a risky asset. The log returns of assets are modulated by a weak or higher-order Markov chain with finite-state space. In particular, the optimal estimates of the second-order Markov chain and parameters of the model are given in terms of the discrete-time filters for the state of the Markov chain, the number of jumps, occupation time and auxiliary processes. We provide a detailed implementation of the model to a dataset of financial time series along with the analysis of the h-day ahead forecasts. The results of our error analysis suggest that within the dataset studied and considering longer predictive horizons, WHMM gives a better forecasting performance than the traditional HMM.

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    File URL: http://www.sciencedirect.com/science/article/B6VB1-51G29YW-1/2/a32e7647393664e5ccf3846a1a8d6825
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    Bibliographic Info

    Article provided by Elsevier in its journal Economic Modelling.

    Volume (Year): 28 (2011)
    Issue (Month): 1-2 (January)
    Pages: 36-46

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    Handle: RePEc:eee:ecmode:v:28:y:2011:i:1-2:p:36-46

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    Web page: http://www.elsevier.com/locate/inca/30411

    Related research

    Keywords: Higher-order Markov chain Filtering Regime-switching model Parameter estimation Change of reference probability technique Gaussian mixture model;

    References

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    1. Tak-Kuen Siu & Wai-Ki Ching & Eric Fung & Michael Ng, 2007. "Extracting Information from Spot Interest Rates and Credit Ratings using Double Higher-Order Hidden Markov Models," Computational Economics, Society for Computational Economics, vol. 29(3), pages 425-425, May.
    2. Turner, C.M. & Startz, R. & Nelson, C.R., 1989. "The Markov Model Of Heteroskedasticity, Risk And Learning In The Stock Market," Working Papers 89-01, University of Washington, Department of Economics.
    3. Bollen, Nicolas P. B. & Gray, Stephen F. & Whaley, Robert E., 2000. "Regime switching in foreign exchange rates: Evidence from currency option prices," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 239-276.
    4. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
    5. Christopher M. Turner & Richard Startz & Charles R. Nelson, 1989. "A Markov Model of Heteroskedasticity, Risk, and Learning in the Stock Market," NBER Working Papers 2818, National Bureau of Economic Research, Inc.
    6. Elliott, R. J. & Malcolm, W. P. & Tsoi, Allanus H., 2003. "Robust parameter estimation for asset price models with Markov modulated volatilities," Journal of Economic Dynamics and Control, Elsevier, vol. 27(8), pages 1391-1409, June.
    7. 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.
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    Cited by:
    1. Sun, Qi & Xu, Weijun & Xiao, Weilin, 2013. "An empirical estimation for mean-reverting coal prices with long memory," Economic Modelling, Elsevier, vol. 33(C), pages 174-181.
    2. Xu, Weijun & Sun, Qi & Xiao, Weilin, 2012. "A new energy model to capture the behavior of energy price processes," Economic Modelling, Elsevier, vol. 29(5), pages 1585-1591.

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