CONSISTENT ESTIMATION OF THE ASYMPTOTIC COVARIANCE STRUCTURE OF MULTIVARIATE SERIAL CORRELATIONS

Guy Melard, Marianne Paesmans and Roch Roy

Journal of Time Series Analysis, 1991, vol. 12, issue 4, 351-361

Abstract: Abstract. A method is proposed for estimating, in a consistent way, the asymptotic covariance structure of serial correlations for a multivariate second‐order stationary process. To obtain a consistent estimator of this structure, which is also of the non‐negative definite type, results relative to the scalar case are generalized. The method consists in weighting appropriately the elements of the sample autocorrelation matrices in a generalization of Bartlett's formula so that the estimator converges in probability. Several useful applications of the results of the paper are mentioned.

Date: 1991
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