Previous article Next article On the Bilateral Prediction Error Matrix of a Multivariate Stationary Stochastic ProcessA. G. Miamee and H. SalehiA. G. Miamee and H. Salehihttps://doi.org/10.1137/0510023PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractA formula for the bilateral prediction error matrix of a multivariate stationary stochastic process in terms of the spectral density and its generalized inverse is given.[1] A. N. Kolmogoroff, Stationary sequences in Hilbert's space, Bolletin Moskovskogo Gosudarstvenogo Universiteta. Matematika, 2 (1941), 40pp, (In Russian.) MR0009098 Google Scholar[2] A. Makagon and , A. Weron, Wold-Cramér concordance theorems for interpolation of q-variate stationary processes over locally compact Abelian groups, J. Multivariate Anal., 6 (1976), 123–137 10.1016/0047-259X(76)90024-5 MR0426126 0332.60026 CrossrefISIGoogle Scholar[3] P. Masani, U. Grenander, Cramér's theorem on monotone matrix-valued functions and the Wold-decomposition, Probability and statistics: The Harald Cramér volume (edited by Ulf Grenander), Almquist & Wiksell, Stockholm, 1959, 175–189 MR0124929 0095.12501 Google Scholar[4] P. Masani, The prediction theory of multivariate stochastic processes. III. Unbounded spectral densities, Acta Math., 104 (1960), 141–162 MR0121952 0096.11505 CrossrefISIGoogle Scholar[5] James B. Robertson and , Milton Rosenberg, The decomposition of matrix-valued measures, Michigan Math. J., 15 (1968), 353–368 10.1307/mmj/1029000039 MR0239044 0167.14602 CrossrefISIGoogle Scholar[6] Habib Salehi, Application of the Hellinger integrals to q-variate stationary stochastic processes, Ark. Mat., 7 (1968), 305–311 (1968) MR0236991 0164.19001 CrossrefISIGoogle Scholar[7] Habib Salehi and , John K. Scheidt, Interpolation of q-variate weakly stationary stochastic processes over a locally compact abelian group, J. Multivariate Anal., 2 (1972), 307–331 10.1016/0047-259X(72)90019-X MR0326833 0243.60027 CrossrefGoogle Scholar[8] N. Wiener and , P. Masani, The prediction theory of multivariate stochastic processes. I. The regularity condition, Acta Math., 98 (1957), 111–150 MR0097856 0080.13002 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Canonical correlation and reduction of multiple time seriesAnnals of the Institute of Statistical Mathematics, Vol. 46, No. 4 | 1 Jan 1994 Cross Ref On the predictor of non-full-rank bivariate stochastic processesJournal of Multivariate Analysis, Vol. 29, No. 1 | 1 Apr 1989 Cross Ref On Determining the Predictor of Nonfull-Rank Multivariate Stationary Random ProcessesA. G. MiameeSIAM Journal on Mathematical Analysis, Vol. 18, No. 4 | 17 July 2006AbstractPDF (818 KB) Volume 10, Issue 2| 1979SIAM Journal on Mathematical Analysis217-445 History Submitted:27 May 1977Published online:17 February 2012 InformationCopyright © 1979 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0510023Article page range:pp. 247-252ISSN (print):0036-1410ISSN (online):1095-7154Publisher:Society for Industrial and Applied Mathematics