Statistical estimation of nonstationary Gaussian processes with long range dependence and intermittency

Abstract

This paper considers statistical inference for nonstationary Gaussian processes with long-range dependence and intermittency. The existence of such a process has been established by Anh et al. (J. Statist. Plann. Inference 80 (1999) 95-110). We systematically consider the case where the spectral density of nonstationary Gaussian processes with stationary increments is of a general and flexible form. The spectral density function of fRBm is thus a special case of this general form. A continuous version of the Gauss-Whittle objective function is proposed. Estimation procedures for the parameters involved in the spectral density function are then investigated. Both the consistency and the asymptotic normality of the estimators of the parameters are established. In addition, a real example is presented to demonstrate the applicability of the estimation procedures.