Unit Root Tests in Three-Regime Setar Models

Abstract

This paper proposes a simple direct testing procedure to distinguish a linear unit root process from a globally stationary three-regime self-exciting threshold autoregressive process. We derive the asymptotic null distribution of the Wald statistic, and show that it does not depend on unknown fixed threshold values. Monte Carlo evidence clearly indicates that the exponential average of the Wald statistic is more powerful than the Dickey-Fuller test that ignores the threshold nature under the alternative.

Keywords: Self-exciting Threshold Autoregressive Models, Unit Roots, Globally Stationary Processes, Threshold Cointegration, Wald Tests, Monte Carlo Simulations, Real Exchange Rates

JEL Classification: C12, C13, C32