Confidence intervals for the long memory parameter based on wavelets and resampling

The problem of constructing confidence intervals for the long-memory parameter of stationary Gaussian processes with long-range dependence is studied. The focus is on confidence intervals for the wavelet estimator introduced by Abry and Veitch (1998). An approximation to the distribution of the estimator based on subsampling is proposed. Such an approximation is used to construct confidence intervals for the long-memory parameter. The performance of these confidence intervals, in terms of both coverage probability and length, is studied by using a Monte Carlo simulation. The proposed confidence intervals have more accurate coverage probability than the method of Veitch and Abry (1999), and are easy to compute in practice.