Cross‐validation Criteria for Setar Model Selection

Three cross‐validation criteria, denoted by respectively C, Cc, and Cu, are proposed for selecting the orders of a self‐exciting threshold autoregressive (SETAR) model when both the delay and the threshold value are unknown. The derivation of C is within a natural cross‐validation framework. The criterion Cc is similar in spirit as AICc, a bias‐corrected version of AIC for SETAR model selection introduced by Wong and Li (1998). The criterion Cu is a variant of Cc having a similar poperty as AICu, a model selection proposed by McQuarrie et al. (1997) for linear models. In a Monte Carlo study, the performance of each of the criteria C, Cc, Cu, AIC, AICc, AICu, and BIC is investigated in detail for various models and various sample sizes. It will be shown that Cu consistently outperforms all other criteria when the sample size is moderate to large.