Asymptotics for Markov chain mixture detection

Matthew Fitzpatrick and Michael Stewart

Econometrics and Statistics, 2022, vol. 22, issue C, 56-66

Abstract: Sufficient conditions are provided under which the log-likelihood ratio test statistic fails to have a limiting chi-squared distribution under the null hypothesis when testing between one and two components under a general two-component mixture model, but rather tends to infinity in probability. These conditions are verified when the component densities describe continuous-time, discrete-state-space Markov chains and the results are illustrated via a parametric bootstrap simulation on an analysis of the migrations over time of a set of corporate bonds ratings. The precise limiting distribution is derived in a simple case with two states, one of which is absorbing which leads to a right-censored exponential scale mixture model. In that case, when centred by a function growing logarithmically in the sample size, the statistic has a limiting distribution of Gumbel extreme-value type rather than chi-squared.

Keywords: Markov chain; Mixture model; Asymptotics (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecosta:v:22:y:2022:i:c:p:56-66

DOI: 10.1016/j.ecosta.2021.11.004

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