Journal
BIOMETRICS
Volume 60, Issue 2, Pages 444-450Publisher
WILEY
DOI: 10.1111/j.0006-341X.2004.00189.x
Keywords
goodness-of-fit; hidden Markov model; model selection; multiple sclerosis; probability plot; stationary time series
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In this article, we propose a graphical technique for assessing the goodness-of-fit of a stationary hidden Markov model (HMM). We show that plots of the estimated distribution against the empirical distribution detect lack of fit with high probability for large sample sizes. By considering plots of the univariate and multidimensional distributions, we are able to examine the fit of both the assumed marginal distribution and the correlation structure of the observed data. We provide general conditions for the convergence of the empirical distribution to the true distribution, and demonstrate that these conditions hold for a wide variety of time-series models. Thus, our method allows us to compare not only the fit of different HMMs, but also that of other models as well. WE! illustrate our technique using a multiple sclerosis data set.
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