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- W4242748696 abstract "Let { x t } be a discrete-time multivariate stationary process possessing an infinite autoregressive representation and let Γ B ( k ), Γ F ( k ) and Γ be the block Toeplitz covariance matrices of x B ( k ) = [ x ′ –1 , x′ –2 , · ··, x ′ – k ]′, x F ( k ) = [ x ′ 1 , x ′ 2 · ·· x ′ k ] and x = [·· · x ′ –2 , x ′ –1 , x ′ 0 , x ′ 1 , x ′ 2 · ··]′ respectively, where k ≧ 1, is finite or infinite. Also let φ m , n ( j ) and δ m , n ( u ) be the coefficients of x t + j and x t – u respectively in the linear least-squares interpolator of x t from x t + 1 , · ··, x t + m ; x t − 1 , · ··, x t – n , where m, n ≧ 0, 0 ≦ j ≦ m , 0 ≦ u ≦ n are integers, z t ( m, n ) denote the interpolation error and τ 2 ( m, n ) = E [ z t ( m, n ) z t ( m, n )′]. A physical interpretation for the components of Γ B ( k ) –1 , Γ F ( k ) –1 and Γ –1 is given by relating these components to the φ m,n ( j ) δ m,n ( u ) and τ 2 ( m, n ). A similar result is shown to hold also for the estimators of Γ B ( k ) –l and the interpolation parameters when these have been obtained from a realization of length T of { x t }. Some of the applications of the results are considered." @default.
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- W4242748696 date "1990-03-01" @default.
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- W4242748696 title "On a relationship between the inverse of a stationary covariance matrix and the linear interpolator" @default.
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- W4242748696 doi "https://doi.org/10.2307/3214603" @default.
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