Testing for unit roots based on sample autocovariances

Abstract

Summary We propose a new unit-root test for a stationary null hypothesis $H_0$ against a unit-root alternative $H_1$. Our approach is nonparametric as $H_0$ assumes only that the process concerned is $I(0)$, without specifying any parametric forms. The new test is based on the fact that the sample autocovariance function converges to the finite population autocovariance function for an $I(0)$ process, but diverges to infinity for a process with unit roots. Therefore, the new test rejects $H_0$ for large values of the sample autocovariance function. To address the technical question of how large is large, we split the sample and establish an appropriate normal approximation for the null distribution of the test statistic. The substantial discriminative power of the new test statistic is due to the fact that it takes finite values under $H_0$ and diverges to infinity under $H_1$. This property allows one to truncate the critical values of the test so that it has asymptotic power 1; it also alleviates the loss of power due to the sample-splitting. The test is implemented in $\texttt{R}$.