Evaluating Unit Root Tests in Heteroscedastic Time Series: A Comparative Study Using Monte Carlo

Abstract

Deciding on which unit root test to use is a topic of active interest. This study compares three unit root tests; the self-normalized, the bootstrap, and the Phillips-Perron (PP) unit root tests in identifying nonstationarity (or stationarity) in time series data with conditional heteroscedasticity. We use a Monte Carlo simulation framework with an AR(1)-GARCH(1,1), MA(1)-GARCH(1,1) and ARMA-GARCH(1,1) data-generating processes to evaluate the performance of unit root tests across different configurations of GARCH parameters, persistence levels, and sample sizes. Through simulation results, the self-normalized (SN) test is the most effective choice followed by the bootstrap when inference heavily relies on identifying near-unit-root behavior in heteroscedastic settings of AR(1)-GARCH(1,1). The best choice under MA(1)-GARCH(1,1) is the PP test followed by the SN test. Under the ARMA(1,1)-GARCH(1,1), both SN and PP tests exhibit strong power for negative MA coefficients, but suffer size for negative coefficients. The Boot test lags in power but shows stable size properties.