Using the bootstrap for finite sample confidence intervals of the log periodogram regression

Abstract

Log periodogram regression is widely applied in empirical applications to estimate the memory parameter, d , of long memory time series. This estimator is consistent for d < 1 and pivotal asymptotically normal for d < 3 / 4 . However, the asymptotic distribution is a poor approximation of the (unknown) finite sample distribution if the sample size is small. Finite sample improvements in the construction of confidence intervals can be achieved by different nonparametric bootstrap procedures based on the residuals of log periodogram regression. In addition to the basic residual bootstrap, the local and block bootstraps seem adequate for replicating the structure that may arise in the errors of the regression when the series shows weak dependence in addition to long memory. The performances of different bias correcting bootstrap techniques and a bias reduced log periodogram regression are also analyzed with a view to adjusting the bias caused by that structure. Finally, an application to the Nelson and Plosser US macroeconomic data is included.