Semiparametric estimation in perturbed long memory series

Abstract

The estimation of the memory parameter in perturbed long memory (LM) series has recently attracted attention. This has been mainly motivated by the adequacy of LM signal plus noise processes to model the behaviour of many financial and economic time series. In this context frequency domain semiparametric techniques are natural choices for the estimation of the memory parameter of the persistent signal. A new extension of the log periodogram regression that explicitly accounts for the added noise is proposed and its properties are compared with other existing techniques. A reduction of the asymptotic bias and a faster convergence are achieved because a larger bandwidth is permitted. Monte Carlo results confirm the bias reduction in finite samples. An application to a series of returns of the Spanish Ibex35 stock index is finally included.