A Nonparametric Test for Detecting Univariate Self-Exciting Threshold Autoregressive (SETAR)-Type Nonlinearity in Time Series

Abstract

A number of parametric tests for detecting SETAR (self-exciting threshold autoregressive) - type nonlinearity have been developed in the literature including those of Keenan (1985), Petrucelli and Davies (1986), Tsay (1986, 1989) and Luukkonen et al. (1988). These tests are test-based approaches which require distribution of the particular parametric test. In this paper, a nonparametric test procedure for testing SETAR-type nonlinearity is proposed. The nonparametric test procedure is based on the concept of a model selection criterion, the Akaike’s information criterion (AIC), in which the problem of detecting the presence of threshold effects is viewed as a model selection problem among two competing models given by the linear specification and its threshold counterpart. The performance of the proposed test is evaluated by means of simulations. The merits, in terms of size and power, of the proposed test are evaluated relative to Keenan’s test and Tsay’s F test. The simulation results indicate that the proposed nonparametric test has comparable power to the parametric tests when the entire data generating process is securely stationary and the sample sizes are sufficiently large.