Asymptotic analysis of model selection criteria for general hidden Markov models

Shouto Yonekura, Alexandros Beskos and Sumeetpal S. Singh

Stochastic Processes and their Applications, 2021, vol. 132, issue C, 164-191

Abstract: The paper obtains analytical results for the asymptotic properties of Model Selection Criteria – widely used in practice – for a general family of hidden Markov models (HMMs), thereby substantially extending the related theory beyond typical ‘i.i.d.-like’ model structures and filling in an important gap in the relevant literature. In particular, we look at the Bayesian and Akaike Information Criteria (BIC and AIC) and the model evidence. In the setting of nested classes of models, we prove that BIC and the evidence are strongly consistent for HMMs (under regularity conditions), whereas AIC is not weakly consistent. Numerical experiments support our theoretical results.

Keywords: Hidden Markov models; Akaike information criteria; Bayesian information criteria; Model evidence (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:132:y:2021:i:c:p:164-191

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DOI: 10.1016/j.spa.2020.10.006

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