A frequency domain bootstrap for Whittle estimation under long-range dependence

Abstract

Whittle estimation is a common technique for fitting parametric spectral density functions to time series, in an effort to model the underlying covariance structure. However, Whittle estimators from long-range dependent processes can exhibit slow convergence to their Gaussian limit law so that calibrating confidence intervals with normal approximations may perform poorly. As a remedy, we study a frequency domain bootstrap (FDB) for approximating the distribution of Whittle estimators. The method provides valid distribution estimation for a broad class of stationary, long-range (or short-range) dependent linear processes, without stringent assumptions on the distribution of the underlying process. A large simulation study shows that the FDB approximations often improve normal approximations for setting confidence intervals for Whittle parameters in spectral models with strong dependence.