A simple test of changes in mean in the possible presence of long-range dependence

We propose a simple testing procedure to test for a change point in the mean of a possibly long-range dependent time series. Under the null hypothesis, the series is stationary with long-range dependence and our test statistic converges to a non-degenerate distribution, whereas under the alternative, the series has a change point in the mean and the test statistic diverges to infinity. We demonstrate the good size and power properties of our test via simulations and illustrate its usefulness by analysing two real data sets.