Hidden Markov Models for Discrete-Valued Time Series

Authored by: Iain L. MacDonald , Walter Zucchini

Handbook of Discrete-Valued Time Series

Print publication date:  December  2015
Online publication date:  January  2016

Print ISBN: 9781466577732
eBook ISBN: 9781466577749
Adobe ISBN:

10.1201/b19485-16

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Abstract

In the search for useful models for discrete-valued time series, one possible approach is to take a standard model for continuous-valued series, for example, a Gaussian autoregressive moving-average process, and to modify or adapt it in order to allow for the discrete nature of the data. Another approach, the one followed here, is to start from a model for discrete data which assumes independence and then to relax the independence assumption by allowing the distribution of the observations to switch among several possibilities according to a latent Markov chain. To take a simple example, a sequence of independent Poisson random variables with common mean would be inappropriate for a series of unbounded counts displaying significant autocorrelation. But a model that allowed the observations to be Poisson with mean either λ1 or λ2, the choice being made by a discrete-time Markov chain, might well be adequate; a model of this kind, it will be seen, allows for both serial dependence and overdispersion relative to the Poisson.

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