Paper Review:

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Paper Review Parameter Estimation in a
Stochastic Drift Hidden Markov Model with a Cap
byJ. Hernandez, D. Saunders L. Seco

• Anatoliy Swishchuk
• Math Comp Finance Lab,
• Dept of Math Stat, U of C
• Lunch at the Lab Talk
• February 3, 2006

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Model
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Interpretation of the Model and Specification
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Difference Between this Model and Pilipovich Model
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Mixing Coefficients
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Mixing Lemma
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Transition Probabilities and Space
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Mixing Coefficients Through P_t
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Infinitesimal Generator
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Spectral Gap Inequality
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Spectral Gap
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Definition of Hidden Markov Model
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Ergodicity and Mixing
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Stationarity and Hidden Markov Model
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Hidden Markov Model
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Assumptions I-III
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Assumption IV
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Main Result
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Follows from the Birkhoffs Ergodic Result
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An Example the Ornstein-Uhlenbeck Model
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Transformation
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Matrix Form
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Another Expression
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Gaussian Distribution
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Transition Probability
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Limits for Mean and for Covariance Matrix
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Gaussian Stationary Distribution
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Convergence
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To Study the Law of the Process Y
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Process y(th)
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Joint Distribution of Y_t and Y_th
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Estimation of Parameters
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(No Transcript)
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Final Calculation of Parameters
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References
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References (cntd)