Estimation of a stationary multivariate ARFIMA process

Abstract

In this note, we consider an m-dimensional stationary multivariate long memory ARFIMA (AutoRegressive Fractionally Integrated Moving Average) process, which is defined as : A(L)D(L) (y₁(t),...,y_m(t))' = B(L) (∈₁(t),..., ∈_m(t))', where M' denotes the transpose of the matrix M. We determine the minimum Hellinger distance estimator (MHDE) of the parameters of a stationary multivariate long memory ARFIMA. This method is based on the minimization of the Hellinger distance between the random function of f_n(.) and a theoretical probability density f_θ(.). We establish, under some assumptions, the almost sure convergence of the estimator and its asymptotic normality.

Keywords: Stationary Multivariate ARFIMA process; Estimation; Long memory; Minimum Hellinger distance

AMS 2010 Mathematics Subject Classification: 62F12, 62H12