Percentage Points of Likelihood Ratio Tests for Threshold Autoregression

Abstract

SUMMARY Likelihood ratio tests for threshold autoregression have been considered by Chan, and Chan and Tong. However, except for the simplest case, percentage points of the (asymptotic) null distribution of the test statistic have not been tabulated. The purpose of this paper is to tabulate the approximate upper percentage points for the general case. This is done via the Poisson clumping heuristic developed by Aldous. Monte Carlo experiments show that the approximation is quite good. As an illustration, the test is then applied to two data sets.