The impact of GARCH on asymmetric unit root tests

Using Monte Carlo simulation, threshold autoregressive (TAR) and momentum-threshold autoregressive (MTAR) asymmetric unit root tests are examined in the presence of generalised autoregressive conditional heteroskedasticity (GARCH). It is shown that TAR and MTAR unit root tests exhibit greater size distortion than the original (implicitly symmetric) Dickey–Fuller unit root test when applied to series exhibiting GARCH. Importantly, it is found that the use of 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 positively dependent upon the size of the volatility parameter of the GARCH model. The relevance of the simulation analysis conducted is supported by GARCH modelling of the term structure of US interest rates. The results of the current analysis 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. The paper concludes by suggesting future areas of research prompted by the present findings.