A Dissertation submitted to the Faculty of Science, University of the Witwatersrand,
Johannesburg, in ful lment of the requirements for the degree of Master of Science.
Johannesburg, 2016. / 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. / LG2017
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/21675 |
| Date | January 2016 |
| Creators | Hoff, Michael Ryan |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | Online resource (xii, 275 leaves), application/pdf |
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