Bootstrapping the log-periodogram estimator of the long-memory parameter: is it worth weighting

Abstract

Estimation of the long-memory parameter from the log-periodogram (LP) regression, due to Geweke and Porter-Hudak (GPH), is a simple and frequently used method of semi-parametric estimation. However, the simple LP estimator suffers from a finite sample bias that increases with the dependency in the short-run component of the spectral density. In a modification of the GPH estimator, Andrews and Guggenberger, AG (2003) suggested a bias-reduced estimator, but this comes at the cost of inflating the variance. To avoid variance inflation, Guggenberger and Sun (2004, 2006) suggested a weighted LP (WLP) estimator using bands of frequencies, which potentially improves upon the simple LP estimator. In all cases a key parameter in these methods is the need to choose a frequency bandwidth, m, which confines the chosen frequencies to be in the ‘neighbourhood’ of zero. GPH suggested a ‘square-root’ rule of thumb that has been widely used, but has no optimality characteristics. An alternative, due to Hurvich and Deo (1999), is to derive the root mean square error (rmse) optimising value of m, which depends upon an unknown parameter, although that can be consistently estimated to make the method feasible. More recently, Arteche and Orbe (2009a,b), in the context of the GPH estimator, suggested a promising bootstrap method, based on the frequency domain, to obtain the rmse value of m that avoids estimating the unknown parameter. We extend this bootstrap method to the AG and WLP estimators and to consideration of bootstrapping in the frequency domain (FD) and the time domain (TD) and, in each case, to ‘blind’ and ‘local’ versions. We undertake a comparative simulation analysis of these methods for relative performance on the dimensions of bias, rmse, confidence interval width and fidelity.