Simulation and estimation for hidden Markov models of Brownian motion

Abstract

This thesis examines methods of simulation and parameter estimation for hidden Markov models. In Chapter 2, we set out the framework of the hidden Markov model and discusses the various problem of interests in modelling. We give procedures for implementing these solutions in practice. In Chapter 3, we discuss the expectation-maximisation (EM) algorithm. This algorithm provide the framework for parameters estimation of a hidden Markov model when the state space of the observations can be discrete or continuous. In Chapter 4, we look at an application of hidden Markov model to the hidden Markov Brownian motion model. Numerical examples are introduced for two and three state Markov chains. Comparison of the results for the simulation and the actual values are made. All computations and simulations were done using SPLUS. The code is given in the appendix.