Bootstrap Test Mean Change Point in Long Memory Time Series

Abstract

Bootstrap plays an important role in change point analysis for it is a data driving method and can avoid estimate some redundant parameters. In this paper, we applied three well known bootstrap methods, the sieve AR bootstrap, the fractional differencing sieve bootstrap and the fractional differencing block bootstrap to test the mean change point in the stationary long memory time series. We use the self normalized ratio statistic as the test statistic and approximate its critical values via these three bootstrap methods. We evaluate the empirical size and power performances of three bootstrap methods. Simulations show that the sieve AR bootstrap undergoes serious size distortions when the long memory parameter nears to 0.5, and the fractional differencing block bootstrap always too conservative compared to the other two bootstrap. The fractional differencing sieve bootstrap, in general, has the best finite sample performance. Finally, we illustrated the method via a set annual discharge data in the Nile River and a set of temperature data in the northern hemisphere.