On the Spectrum of Stationary Gaussian Sequences Satisfying the Strong Mixing Condition. II. Sufficient Conditions. Mixing Rate

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Previous article Next article On the Spectrum of Stationary Gaussian Sequences Satisfying the Strong Mixing Condition. II. Sufficient Conditions. Mixing RateI. A. IbragimovI. A. Ibragimovhttps://doi.org/10.1137/1115002PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. A. Ibragimov, On the spectrum of stationary Gaussian sequences satisfying the strong mixing condition. I. Necessary conditions, Theory Prob. Applications, 10 (1965), 85–106 10.1137/1110008 0131.18101 LinkGoogle Scholar[2] A. N. Kolmogorov and , Yu. A. Rozanov, On strong mixing conditions for stationary Gaussian processes, Theory Prob. Applications, 5 (1960), 204–208 10.1137/1105018 0106.12005 LinkGoogle Scholar[3] Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall Inc., Englewood Cliffs, N. J., 1962xiii+217 MR0133008 0117.34001 Google Scholar[4] A. F. Timan, Theory of Approximation of Functions of a Real Variable, Fizmatgiz, Moscow, 1960, (In Russian.) Google Scholar[5] Henry Helson and , Donald Sarason, Past and future, Math. Scand, 21 (1967), 5–16 (1968) MR0236989 0241.60029 Google Scholar[6] J. Littlewood, A Mathematician's Miscellany, Methuen, London, 1953 0051.00101 Google Scholar[7] G. M. Goluzin, Geometric Theory of Functions of a Complex Variable, Izd-vo “Nauka”, Moscow, 1966, (In Russian.) Google Scholar[8] N. I. Akhiezer, Vorlesungen über Approximations theorie, Akedemic Verlag, Berlin, 1953, (Translated from Russian.) 0052.29002 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Mixed-Norm Spaces and Prediction of S α S Moving Averages27 April 2015 | Journal of Time Series Analysis, Vol. 36, No. 6 Cross Ref On the behavior of the covariance matrices in a multivariate central limit theorem under some mixing conditionsIllinois Journal of Mathematics, Vol. 56, No. 3 Cross Ref A parametric bootstrap test for cyclesJournal of Econometrics, Vol. 129, No. 1-2 Cross Ref A criterion for a continuous spectral densityJournal of Multivariate Analysis, Vol. 86, No. 1 Cross Ref Rational spectral densities and strong mixingJournal of Multivariate Analysis, Vol. 42, No. 2 Cross Ref On the Glivenko–Cantelli theorem for generalized empirical processes based on strong mixing sequencesStatistics & Probability Letters, Vol. 10, No. 5 Cross Ref On the consistency and finite-sample properties of nonparametric kernel time series regression, autoregression and density estimators1 December 1986 | Annals of the Institute of Statistical Mathematics, Vol. 38, No. 3 Cross Ref Nonparametric Time-Series Estimation of Joint DGP, Conditional DGP, and Vector Autoregression18 October 2010 | Econometric Theory, Vol. 1, No. 1 Cross Ref Asymptotic expansions for sums of weakly dependent random vectorsZeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 64, No. 2 Cross Ref NONPARAMETRIC ESTIMATORS FOR TIME SERIESJournal of Time Series Analysis, Vol. 4, No. 3 Cross Ref Maximum likelihood estimates of incorrect Markov models for time series and the derivation of AIC14 July 2016 | Journal of Applied Probability, Vol. 17, No. 1 Cross Ref Volume 15, Issue 1| 1970Theory of Probability & Its Applications History Submitted:05 October 1968Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1115002Article page range:pp. 23-36ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics