MAXIMUM LIKELIHOOD ESTIMATION OF AUTOCOVARIANCE MATRICES FROM REPLICATED SHORT TIME SERIES
S. Degerine · Journal of Time Series Analysis · 1987
Abstract. 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.