Inference for autocorrelations in the possible presence of a unit root

Abstract

We consider the problem of making inference for the autocorrelations of a time series in the possible presence of a unit root. Even when the underlying series is assumed to be strictly stationary, the robustness against a unit root is a desirable property to ensure good finite-sample coverage in case the series has a near unit root. In addition to discussing a confidence interval for the autocorrelation at a given lag, we also consider a simultaneous confidence band for the first k autocorrelations. We suggest the use of the subsampling method applied to properly studentized statistics, which results in confidence intervals and bands with asymptotically correct coverage probability. An application to practical model selection is given, while a simulation study examines finite-sample performance.