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MAXIMUM LIKELIHOOD ESTIMATION OF AUTOCOVARIANCE MATRICES FROM REPLICATED SHORT TIME SERIES
Author(s) -
Degerine Serge
Publication year - 1987
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.1467-9892.1987.tb00428.x
Subject(s) - autocovariance , mathematics , toeplitz matrix , series (stratigraphy) , matrix (chemical analysis) , covariance matrix , sample mean and sample covariance , estimation of covariance matrices , maximum likelihood , computation , statistics , algorithm , mathematical analysis , pure mathematics , paleontology , materials science , fourier transform , estimator , composite material , biology
. The maximum likelihood estimation of an autocovariance matrix based on replicated observations of stationary times series is considered. A sufficient condition for the existence of the estimate, when the sample covariance matrix is singular, is given. An iterative method for its computation is proposed: it is based on some spectral decompositions of Toeplitz matrices. Simulation results show the superiority of the estimate over the usual empirical sample autocovariance matrix.