Tests for a Unit Root Using Three-Regime TAR Models: Power Comparison and Some Applications

Tests for a unit root using three-regime threshold autoregressive (TAR) models play a significant role in the empirical analysis of some economic theories. This article compares the powers of recently proposed unit root tests in three-regime TAR models using Monte Carlo experiments. The following results are obtained from the Monte Carlo simulations: Kapetanios and Shin's (2006) Wsup, Wave, and Wexp statistics, which degenerate with respect to the threshold parameters under the null hypothesis, have a better power in the three-regime TAR process with a relatively narrow band of a unit root process and a small sample, whereas their statistics do not perform well when the threshold and sample size increase; Bec et al.'s (2004, BBC) sup W and Park and Shintani's (2005) inf-t statistics and their restricted models, which do not degenerate with respect to the threshold parameters in the limit, perform poorly in the three-regime TAR process with a small threshold even when compared with the Dickey-Fuller test, whereas their statistics perform better in the case of a large threshold; sup W, inf-t, and their restricted models perform much better when the sample size and threshold increase and the outer regimes have a rapid convergence. In order to substantiate the use of our Monte Carlo results for some of the applied work, we apply these tests to the real exchange rates for many countries.