Monitoring a change in persistence of a long range dependent time series

We consider the detection of a change in persistence of a long range dependent time series. The usual approach is to use one-shot tests to detect a change in persistence a posteriori in a historical data set. However, as breaks can occur at any given time and data arrives steadily it is desirable to detect a change in persistence as soon as possible. We propose the use of a MOSUM type test which allows sequential application whenever new data arrives. We derive the asymptotic distribution of the test statistic and prove consistency. We further study the finite sample behavior of the test and provide an empirical application.