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

Abstract

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.Power, Three-regime TAR model, Unit root test,

Unit Root Tests in Time Series Volume 2

“…For example, see Maki (2009) for a review and assessment of unit root tests in a three regime model, and Battaglia and Protopapas (2010), who considered both nonlinearity and nonstationarity and allow the regime switching to be self-exciting, smooth transition or piecewise linear. Threshold models can be extended to the variance as in TAR versions of ARCH (TARCH) models (see, for example, Baragona and Cucina, 2008).…”

“…For example, Maki (2009) undertakes a simulation study of a number of unit root tests in a 3RTAR and searches from the 5% to the 45% quantiles for the lower threshold, κ 1 , and from the 55% to the 95% quantile for the upper threshold, κ 2 , so that there are never less than 10% of the observations in the inner regime. To the author's knowledge, the limiting null distribution of these Wald-type tests has not yet been obtained, so that quantiles for testing need to be obtained by simulation or bootstrapping, which ties in with Maki's (2009) recommendation to use size-adjusted critical values for the various tests. (See Bec, Ben Salem and Carrasco, 2004, theorem 2, for the general form of the limiting distribution.)…”

“…Ceteris paribus, the power of all the tests declines monotonically as the threshold band increases. For a more extensive power comparison using size-adjusted power see Maki (2009), who also included a one-sided t-type test due to Park and Shintani (2005), which performed well but did not dominate the other tests.…”

Unit roots, non-linearities and structural breaks

“…The test allows for a general dependence structure in the errors and uses the residual-block bootstrap procedure (see Paparoditis and Politis 2003) to calculate asymptotic p-values. Comparative studies are, amongst others, Maki (2009) and Choi and Moh (2007).…”

“…We refer to the paper by Cavaliere and Taylor (2007) for details about the numerical procedure. Finally, bootstrap tests for a unit root under non-stationary volatility have been suggested by Chang and Park (2003), Park (2003), Cavaliere and Taylor (2007, 2008, 2009 among others.…”