Distinguishing between breaks in the mean and breaks in persistence under long memory

A procedure to discriminate between stationarity, a break in the mean and a break in persistence in a time series that may exhibit long memory is introduced. The asymptotic properties of test statistics based on the CUSUM statistic are studied. In a Monte Carlo study we further analyze the finite sample properties of the procedure. An application to inflation rates shows the potential of our procedure for future research. •A two-step procedure to distinguish breaks in mean and breaks in persistence under long memory is introduced.•The procedure employs a CUSUM-based test statistic.•The finite sample properties of the procedure are studied by a Monte Carlo simulation.