Detection of change in persistence of a linear time series

This paper studies how to detect structural change characterized by a shift in persistence of a time series. In particular, we are interested in a process shifting from stationarity to nonstationarity or vice versa. A general linear process is considered that includes an ARMA process as a special one. We derive a statistic for testing the occurrence of such a change and investigate asymptotic behavior of it. We show that our test has power against fairly general alternatives of change in persistence. A Monte Carlo study shows that our test has reasonably good size and power properties in finite samples. We also discuss how to estimate the unknown period of change. We apply our test to two examples of time series, the series of the U.S. inflation rate and the series of U.S. federal governmentʹs budget deficit in the postwar period. For these two series we have found strong evidence of structural change from stationarity to nonstationarity.