Broadband semi-parametric estimation of long-memory time series by fractional exponential models

This article proposes broadband semi-parametric estimation of a long-memory parameter by fractional exponential (FEXP) models. We construct the truncated Whittle likelihood based on FEXP models in a semi-parametric setting to estimate the parameter and show that the proposed estimator is more efficient than the FEXP estimator by Moulines and Soulier (1999) in linear processes. A Monte Carlo simulation suggests that the proposed estimation is more preferable than the existing broadband semi-parametric estimation.