Monitoring change in persistence in linear time series

A moving ratio monitoring scheme is proposed to detect changes between trend stationary (I(0)I(0)) and difference stationary (I(1)I(1)) regimes. It is consistent both for I(1)I(1) to I(0)I(0) and I(0)I(0) to I(1)I(1) change, and has less computation time. The empirical size, power and average run length of the test are evaluated in a simulation study. Simulations indicate that the new method achieves a far superior finite sample performance as compared with the existing variance ratio monitoring procedure in the literature. A modified version is also considered under I(0)I(0) null hypothesis in the presence of a variance shift. In addition, we apply the procedure to investigate the US inflation rate data and show how it is used to detect multiple changes in persistence.