n South African Actuarial Journal - Hidden Markov Models for Time Series : An Introduction using R, Walter Zucchini and Iain L. MacDonald : book review

Volume 10, Issue 1
  • ISSN : 1680-2179


Hidden Markov models (HMMs) are statistical models in which the distribution that generates the observation depends on the state of an underlying but unobserved Markov process. They provide a general approach to modelling apparently non-stationary time series, where the non-stationarity originates from an underlying Markov process influencing the distribution of the observations.

An example used extensively in the book is the annual number of major earthquakes (magnitude 7 or greater) in the world over the period 1900 to 2006. An HMM analysis suggests that the number occurring in any year has a Poisson distribution, the average number varying according to a Markov process with three (or possibly four) states, presumably corresponding to different states of the Earth's crust. A corresponding example from the actuarial field could be the number of major accident claims received by an insurance company in a year. Here the different states of the Markov process (if indeed an HMM is appropriate) could correspond to different states of the world security. Many other examples are provided in the text.

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