1. Paper Review: “Parameter Estimation in a Stochastic Drift Hidden Markov Model with a Cap” by J. 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

2. Model

3. Interpretation of the Model and Specification

4. Difference Between this Model and Pilipovich Model

5. Mixing Coefficients

6. Mixing Lemma

7. Transition Probabilities and Space

8. Mixing Coefficients Through P_t

9. Infinitesimal Generator

10. Spectral Gap Inequality

11. Spectral Gap

12. Definition of Hidden Markov Model

13. Ergodicity and Mixing

14. Stationarity and Hidden Markov Model

15. Hidden Markov Model

16. Assumptions I-III

17. Assumption IV

18. Main Result

19. Follows from the Birkhoff’s Ergodic Result

20. An Example: the Ornstein- Uhlenbeck Model

21. Transformation

22. Matrix Form

23. Another Expression

24. Gaussian Distribution

25. Transition Probability

26. Limits for Mean and for Covariance Matrix

27. Gaussian Stationary Distribution

28. Convergence

29. To Study the Law of the Process Y

30. Process y(t+h)

31. Joint Distribution of Y_t and Y_{t+h}

32. Estimation of Parameters

34. Final Calculation of Parameters

35. References

36. References (cntd)