Model Selection in Threshold Models

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On the least squares estimation of multiple-regime threshold autoregressive models (2012, methodology): “More information criteria as model selection tools for nonlinear threshold models, see Kapetanios (2001), in which the author established the consistency of lag selection and compared the small sample performance among different criteria. For the choice of m, Gonzalo and Pitarakis (2002) proposed a ”
ON THE DETERMINATION OF THE NUMBER OF REGIMES IN MARKOV‐SWITCHING AUTOREGRESSIVE MODELS (2002, background): “…2001), r̂will beweakly or strongly consistent for r under the conditions on the penalty factor CT dim(Hk) given in Theorems 3 and 4, respectively, of Kapetanios (2001), assuming the maximum state dimension (k*) allowed for in (2) is not smaller than the true state dimension (r).4 It is worth…”