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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

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.

Suggested Citation

  • Xi, Xiaojing & Mamon, Rogemar, 2011. "Parameter estimation of an asset price model driven by a weak hidden Markov chain," Economic Modelling, Elsevier, vol. 28(1), pages 36-46.
    • Handle: RePEc:eee:ecmode:v:28:y:2011:i:1:p:36-46
    DOI: 10.1016/j.econmod.2010.10.002
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    References listed on IDEAS

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    1. Turner, Christopher M. & Startz, Richard & Nelson, Charles R., 1989. "A Markov model of heteroskedasticity, risk, and learning in the stock market," Journal of Financial Economics, Elsevier, vol. 25(1), pages 3-22, November.
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    Cited by:

    1. Zhu, Dong-Mei & Lu, Jiejun & Ching, Wai-Ki & Siu, Tak-Kuen, 2017. "Discrete-time optimal asset allocation under Higher-Order Hidden Markov Model," Economic Modelling, Elsevier, vol. 66(C), pages 223-232.
    2. Gao, Huan & Mamon, Rogemar & Liu, Xiaoming & Tenyakov, Anton, 2015. "Mortality modelling with regime-switching for the valuation of a guaranteed annuity option," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 108-120.
    3. 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.
    4. Jo~ao Pedro Rodrigues do Carmo, 2018. "Modeling stock markets through the reconstruction of market processes," Papers 1803.06653, arXiv.org.
    5. Xiong, Heng & Mamon, Rogemar, 2019. "A higher-order Markov chain-modulated model for electricity spot-price dynamics," Applied Energy, Elsevier, vol. 233, pages 495-515.
    6. Heng Xiong & Rogemar Mamon, 2018. "Putting a price tag on temperature," Computational Management Science, Springer, vol. 15(2), pages 259-296, June.
    7. Xiaojing Xi & Rogemar Mamon, 2014. "Capturing the Regime-Switching and Memory Properties of Interest Rates," Computational Economics, Springer;Society for Computational Economics, vol. 44(3), pages 307-337, October.
    8. 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.

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