Cross-validation criteria for SETAR model selection

Three cross-validation criteria, denoted C, C_c, and C_u 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 derivatioon of C is within a natural cross-validation framework. The crietion C_c is similar in spirit as AIC_c, a bias-corrected version of AIC for SETAR model selection introduced by Wong and LI (1998). The criterion C_u is a variant of C_c having similar property as AIC_u, a modl selection criterion proposed by McQuarrie et al. (1997) for linear models. In a Monte Carlo study, the performance of each of the criteria C, C_c, C_u, AIC, AIC_c, AIC_u, and BIC is invesigated in detail for various models and various sample sizes. It will be shown that C_u consistently outperforms all other criteria when the sample size is moderate to large.