Log-Periodogram Estimation of the Long-Memory Parameter: An Evaluation of Competing Estimators

This study evaluates a number of methods of reducing the bias and mean squared error of log-periodogram (LP) based methods to estimate the long-memory parameter and, in addition, assesses the actual coverage of the associated confidence intervals, considering both tails and the width of the interval. This is critical as previous results concentrating on two-sided intervals may mask severe distortion in one tail. The evaluation includes: developments of the Geweke and Porter-Hudak (GPH) method due to Hurvich and Deo (1999) and Andrews and Guggenberger (AG, 2003); the weighted LP, WLP, estimator due to Guggenberger and Sun (GS, 2004, 2006); and a frequency-based bootstrap method to improve estimator performance. A central problem in the application of these methods is the selection of the number of frequencies, m, to be included in the LP regression. A frequently used, but generally unsatisfactory, solution is to use a fixed number of frequencies of the form m = n^alpha where, for example, alpha = 0.5 (the square-root rule) or 0.7; in contrast we use a plug-in method to obtain a feasible first-order bias reduced estimator. Including infeasible, feasible and bootstrapped variations, 11 estimators are considered and the simulations suggest that whilst there is no single dominant estimation method, the bootstrapped versions associated with each method generally offer significant gains over the standard versions for coverage rate accuracy. Overall, the bootstrapped WLP estimator is superior for ‘moderate’ serial correlation in the short-run dynamics and offers a significant reduction in the average width of the confidence intervals. The results are illustrated with data on the Nile river flow and the gold-silver price.