Testing a Time Series for Difference Stationarity

Abstract

This paper addresses the problem of testing the hypothesis that an observed series is difference stationary. The alternative hypothesis is that the series is another nonstationary process; in particular, an autoregressive model with a random parameter is used. A locally best invariant test is developed assuming Gaussianity, and a representation of its asymptotic distribution as a mixture of Brownian motions is found. The performance of the test in finite samples is investigated by simulation. An example is given where the difference stationary assumption for a well-known data series is rejected.