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    • University of Missouri-Columbia
    • Graduate School - MU Theses and Dissertations (MU)
    • Theses and Dissertations (MU)
    • Dissertations (MU)
    • 2007 Dissertations (MU)
    • 2007 MU dissertations - Freely available online
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    Volatility estimation and price prediction using a hidden Markov model with empirical study

    Yin, Pei, 1978-
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    Date
    2007
    Format
    Thesis
    Metadata
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    Abstract
    This work provides a solid development of a hidden Markov model (HMM) from the economic insight to the mathematic formulation. In this model, we assume both drift and volatility of the security return process are driven by certain underlying economic forces which evolve together as a finite-state, time-invariant Markov chain. Unfortunately, this chain is unobservable. Through stochastic filtering techniques and EM algorithm with modified iteration steps, we estimate the state space and transition matrix of the Markov chain, as well as the state spaces of the drift and volatility. With these estimates we can smooth and predict the drift and volatility processes and apply them to the security price prediction. On an empirical level, we first use Monte Carlo simulation to show the robustness of our estimates, and then implement HMM on various data sets of historical prices including: major indices, bonds, mutual funds, common stocks, and ETFs to back test the predicability of the model. Moreover, we compare the applicability of HMM with the well established GARCH(1,1) model, as far as the prediction performance is concerned, our results indicate HMM outperforms GARCH(1,1).
    URI
    https://doi.org/10.32469/10355/4795
    https://hdl.handle.net/10355/4795
    Degree
    Ph. D.
    Thesis Department
    Mathematics (MU)
    Rights
    OpenAccess.
    This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.
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    • Mathematics electronic theses and dissertations (MU)
    • 2007 MU dissertations - Freely available online

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