Optimal Tests for Distinguishing PAR Models from PSETAR Models

This paper aims to detect nonlinearity in periodic autoregressive models. We introduce parametric and semiparametric local asymptotic optimal tests designed for distinguishing a periodic autoregressive model from a periodic self-exciting threshold autoregressive (SETAR) model. Leveraging the Local Asymptotic Normality (LAN) property specific to periodic SETAR models, we devise a parametric test that is locally asymptotically most stringent. Additionally, the utilization of kernel estimation for the density function allows the construction of an adaptive test for enhanced flexibility and accuracy in detecting nonlinearity.