Finite-sample properties of asymmetric unit root tests in the presence of GARCH: The impact of alternative methods of threshold selection

The research of Kim and Schmidt (1993) is extended to examine the properties of asymmetric unit root tests in the presence of generalised autoregressive conditional heteroskedasticity (GARCH). Using Monte Carlo simulation, threshold autoregressive and momentum—threshold autoregressive asymmetric unit tests are shown to suffer greater size distortion than the original (implicitly symmetric) Dickey-Fuller test when applied to series exhibiting GARCH. Importantly, it is found that the use consistent-threshold estimation increases the oversizing of the resulting asymmetric unit root test whether based upon the TAR or the MTAR model. The extent of oversizing of all tests considered is shown to be dependent upon the size of the volatility parameter of the GARCH model, with size distortion greater for larger values of the volatility parameter. The relevance of the simulation analysis conducted is supported by GARCH modelling of the term structure of US interest rates, the empirical example considered in the seminal study of Enders and Granger (1998), with the estimated volatility parameter for the GARCH model found to be large enough to generate substantial oversizing for asymmetric unit root tests. The results indicate that if GARCH behaviour is suspected in economic or financial data, practitioners should interpret the results of asymmetric unit root tests with care to avoid drawing a spurious inference of stationarity.