A review and application of hidden Markov models and double chain Markov models

Abstract

Hidden Markov models (HMMs) and double chain Markov models (DCMMs) are classical Markov model extensions used in a range of applications in the literature. This dissertation provides a comprehensive review of these models with focus on i) providing detailed mathematical derivations of key results - some of which, at the time of writing, were not found elsewhere in the literature, ii) discussing estimation techniques for unknown model parameters and the hidden state sequence, and iii) discussing considerations which practitioners of these models would typically take into account. Simulation studies are performed to measure statistical properties of estimated model parameters and the estimated hidden state path - derived using the Baum-Welch algorithm (BWA) and the Viterbi Algorithm (VA) respectively. The effectiveness of the BWA and the VA is also compared between the HMM and DCMM. Selected HMM and DCMM applications are reviewed and assessed in light of the conclusions drawn from the simulation study. Attention is given to application in the field of Credit Risk.