Testing for Multivariate Threshold Autoregression

Abstract

In this article we propose a testing procedure for multivariate threshold autoregression with the disturbances following conditional homoscedastic martingale difference sequences. A right-tailed asymptotic distribution of the proposed test statistics is derived and the accuracy is investigated by simulations. The numerical simulations however show a remarkable robustness to a miss-specification of the order of the AR model. This encourages one to apply the asymptotic results, which will make the computation more convenient in actual applications. Furthermore, some numerical simulations indicate that the proposed test is more powerful than the test in [12]. Key Words: Eigenvalues; Lagrange-multiplier test; Likelihood ratio test; Martingale differences; Threshold autoregression