Asymptotic analysis of model selection criteria for general hidden Markov models

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