A strategy for optimal bandwidth selection in Local Whittle estimation

The Local Whittle estimator is one of the most popular techniques for estimating the memory parameter in long memory series due to its simple implementation and nice asymptotic properties under mild conditions. However, its empirical performance depends heavily on the bandwidth, that is the band of frequencies used in the estimation. Different choices may lead to different conclusions about, for example, the stationarity of the series or its mean reversion. Optimal bandwidth selection is thus of crucial importance for accurate estimation of the memory parameter, but few strategies for assuring this have been proposed to date, and their results in applied contexts are poor. A new strategy based on minimising a bootstrap approximation of the mean square error is proposed here and its performance is shown to be convincing in an extensive Monte Carlo analysis and in applications to real series.