Tests for a Unit Root Using Three-Regime TAR Models: Power Comparison and Some Applications
通过蒙特卡洛实验比较了多种三区制阈值自回归模型单位根检验的功效，发现不同统计量在阈值大小和样本量变化时表现各异，并将这些检验应用于多国实际汇率数据。
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 Kapetanios , G. , Shin , Y. ( 2006 ). Unit root tests in three-regime SETAR models . Econometrics Journal 9 : 252 – 278 .[Crossref], [Web of Science ®] , [Google Scholar]) W sup , W ave , and W exp 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 Bec , F. , Ben Salem , M. , Carrasco , M. ( 2004 ). Tests for unit-root versus threshold specification with an application to the purchasing power parity relationship . Journal of Business and Economic Statistics 22 : 382 – 395 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar], BBC) sup W and Park and Shintani's (2005 Park , J. Y. , Shintani , M. ( 2005 ). Testing for a Unit Root Test Against Transitional Autoregressive Models . Working paper No. 05-W10, Vanderbilt University . [Google Scholar]) 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.