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October 2018 Estimation of a stationary multivariate ARFIMA process
Kévin Stanislas Mbeke, Ouagnina Hili
Afr. Stat. 13(3): 1717-1732 (October 2018). DOI: 10.16929/as/1717.130

Abstract

In this note, we consider an \(m\text{-dimensional}\) stationary multivariate long memory ARFIMA (AutoRegressive Fractionally Integrated Moving Average) process, which is defined as : \(A(L)D(L)\left( y_1(t),\ldots,y_m(t)\right)^{'}= B(L)\left( \varepsilon_1(t),\ldots,\varepsilon_m(t)\right)^{'}\), 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 \(f_{\theta}(.)\). We establish, under some assumptions, the almost sure convergence of the estimator and its asymptotic normality.

Dans cette note, nous considérons un processus ARFIMA (AutoRegressive Fractionally Integrated Moving Average) stationnaire multivarié à longue mémoire défini par : \(A(L)D(L)\left( y_1(t),\ldots,y_m(t)\right)^{'}= B(L)\left( \varepsilon_1(t),\ldots,\varepsilon_m(t)\right)^{'}\), où \(M^{'}\) représente la transposée de la matrice $M$. Nous déterminons le minimum de distance de Hellinger d’un estimateur (MHDE) de paramètres d’un processus ARFIMA stationnaire multivarié à longue mémoire. Cette méthode consiste à minimiser la distance de Hellinger entre la densité de probabilité théorique \(f_{\theta}(.)\) et une fonction ale´atoire \(f_{n}(.)\). Sous quelques hypothèses, nous établissons la convergence presque sûre de l’estimateur et sa normalité asymptotique.

Citation

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Kévin Stanislas Mbeke. Ouagnina Hili. "Estimation of a stationary multivariate ARFIMA process." Afr. Stat. 13 (3) 1717 - 1732, October 2018. https://doi.org/10.16929/as/1717.130

Information

Published: October 2018
First available in Project Euclid: 12 December 2018

zbMATH: 07003213
MathSciNet: MR3887180
Digital Object Identifier: 10.16929/as/1717.130

Subjects:
Primary: 62F12, 62H12

Rights: Copyright © 2018 The Statistics and Probability African Society

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Vol.13 • No. 3 • October 2018
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