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Estimation of a stationary multivariate ARFIMA process

Kévin Stanislas Mbeke, Ouagnina Hili

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),...,ym(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 fn(.) and a theoretical probability density fθ(.). 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




http://dx.doi.org/10.16929/as/1717.130
AJOL African Journals Online