An alternative to the Baum-Welch recursions for hidden Markov models

Details An alternative to the Baum-Welch recursions for hidden Markov models An alternative to the Baum-Welch recursions for hidden Markov models

2011-12-31

arxiv.org/abs/1201.0277v1

Mathematics

Statistics Theory

Scientific paper

We develop a recursion for hidden Markov model of any order h, which allows us to obtain the posterior distribution of the latent state at every occasion, given the previous h states and the observed data. With respect to the well-known Baum-Welch recursions, the proposed recursion has the advantage of being more direct to use and, in particular, of not requiring dummy renormalizations to avoid numerical problems. We also show how this recursion may be expressed in matrix notation, so as to allow for an efficient implementation, and how it may be used to obtain the manifest distribution of the observed data and for parameter estimation within the Expectation-Maximization algorithm. The approach is illustrated by an application to financial data which is focused on the study of the dynamics of the volatility level of log-returns.

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