Evaluating the performance of unit root tests in single time series processes

Abstract

Unit root tests for stationarity have relevancy in almost every practical time series analysis. Deciding on which unit root test to use is a topic of active interest. In this study, we compare the performance of the three commonly used unit root tests (i.e., Augmented Dickey-Fuller (ADF), Phillips-Perron (PP), and Kwiatkowski Phillips Schmidt and Shin (KPSS)) in time series. Based on literature, these unit root tests sometimes disagree in selecting the appropriate order of integration for a given series. Therefore, the decision to use a unit root test relies essentially on the judgment of the researcher. Suppose we wish to annul the subjective decision. In that case, we have to locate an objective basis that unmistakably characterizes which test is the most appropriate for a particular time series type. Thus, this study seeks to unravel this problem by providing a guide on which unit root tests to utilize when there is a disagreement between them. A simulation study of eight (8) univariate time series models with eight (8) different sample sizes, three (3) differencing orders, and nine different parameter values were performed. It was observed from the results that the performance of the three tests improved as the sample size increased. Based on comparing the overall performance, the KPSS was the "best" unit root test to use when there is disagreement.