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Estimation of a stationary multivariate ARFIMA process. (English. French summary) Zbl 1409.62175

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

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62H12 Estimation in multivariate analysis
62F12 Asymptotic properties of parametric estimators
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Full Text: Euclid