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CONSISTENT ESTIMATION OF THE ASYMPTOTIC COVARIANCE STRUCTURE OF MULTIVARIATE SERIAL CORRELATIONS
Author(s) -
Melard Guy,
Paesmans Marianne,
Roy Roch
Publication year - 1991
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1991.tb00089.x
Subject(s) - mathematics , covariance , multivariate statistics , statistics , estimation , estimation of covariance matrices , covariance function , multivariate analysis , matérn covariance function , econometrics , covariance intersection , management , economics
. 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.