Augmented log-periodogram regression in long memory signal plus noise models

The estimation of the memory parameter in perturbed long memory series has recently attracted attention motivated especially by the strong persistence of the volatility of many financial and economic time series and the use of Long Memory in Stochastic Volatility (LMSV) processes to model such a behaviour. This paper proposes an extension of the log periodogram regression which explicitly accounts for the added noise. Contrary the the non linear log periodogram regression of Sun and Phillips (2003), no linear approximation of the logarithmic term which accounts for the noise is used. This produces a reduction of the bias and increases the asymptotic efficiency in long memory signal plus noise series. Asymptotic and finite sample properties of the estimator are analyzed. Finally an application to the Spanish stock index Ibex35 is included.