On Maximum Likelihood Estimation of Parameters of the Spectral Density of Stationary Time Series

Abstract

Previous article Next article On Maximum Likelihood Estimation of Parameters of the Spectral Density of Stationary Time SeriesI. A. IbragimovI. A. Ibragimovhttps://doi.org/10.1137/1112013PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Yu. A. Rozanov, Stationary Random Processes, Fizmatgiz, Moscow, 1963, (In Russian.) Google Scholar[2] P. Whittle, Estimation and information in stationary time series, Ark. Mat., 2 (1953), 423–434 MR0060797 0053.41003 CrossrefGoogle Scholar[3] A. M. Walker, Asymptotic properties of least-squares estimates of parameters of the spectrum of a stationary non-deterministic time-series, J. Austral. Math. Soc., 4 (1964), 363–384 MR0171345 0124.10504 CrossrefGoogle Scholar[4] J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953viii+654 MR0058896 0053.26802 Google Scholar[5] A. F. Timan, Theory of Approximation of Functions of a Real Variable, Fizmatgiz, Moscow, 1960, (In Russian.) Google Scholar[6] I. I. Privalov, Boundary Properties of Analytic Functions, Gostekhizdat, Moscow-Leningrad, 1950, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Limit theorems for Toeplitz-type quadratic functionals of stationary processes and applicationsProbability Surveys, Vol. 19, No. none Cross Ref Statistical Estimation for Stationary Models with Tapered Data13 January 2022 | Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), Vol. 56, No. 6 Cross Ref Sampling properties of color Independent Component AnalysisJournal of Multivariate Analysis, Vol. 181 Cross Ref Statistical inference for stationary linear models with tapered dataStatistics Surveys, Vol. 15, No. none Cross Ref Asymptotic properties of parameter estimates for random fields with tapered dataElectronic Journal of Statistics, Vol. 11, No. 2 Cross Ref Minimum Contrast Method for Parameter Estimation in the Spectral Domain28 December 2013 Cross Ref The trace problem for Toeplitz matrices and operators and its impact in probabilityProbability Surveys, Vol. 11, No. none Cross Ref Minimum contrast estimation of stationary processes based on the squared periodogram∗27 November 2012 | Lithuanian Mathematical Journal, Vol. 52, No. 4 Cross Ref On a Szegö type limit theorem, the Hölder-Young-Brascamp-Lieb inequality, and the asymptotic theory of integrals and quadratic forms of stationary fields29 July 2010 | ESAIM: Probability and Statistics, Vol. 14 Cross Ref Statistical inference using higher-order informationJournal of Multivariate Analysis, Vol. 98, No. 4 Cross Ref Minimum contrast estimation of random processes based on information of second and third ordersJournal of Statistical Planning and Inference, Vol. 137, No. 4 Cross Ref On a class of minimum contrast estimators for fractional stochastic processes and fieldsJournal of Statistical Planning and Inference, Vol. 123, No. 1 Cross Ref Quasi-likelihood-based higher-order spectral estimation of random fields with possible long-range dependence14 July 2016 | Journal of Applied Probability, Vol. 41, No. A Cross Ref Parameter identification for singular random fields arising in Burgers’ turbulenceJournal of Statistical Planning and Inference, Vol. 80, No. 1-2 Cross Ref Bootstrap maximum likelihood estimation of the parameter in spectral density of stationary processesActa Mathematicae Applicatae Sinica, Vol. 12, No. 3 Cross Ref Asymptotic properties of minimum contrast estimators for parameters of boolean modelsMetrika, Vol. 40, No. 1 Cross Ref Identification of non-minimum phase transfer function using higher-order spectrumAnnals of the Institute of Statistical Mathematics, Vol. 44, No. 2 Cross Ref Model fitting for continuous-time stationary processes from discrete-time dataJournal of Multivariate Analysis, Vol. 41, No. 1 Cross Ref A LINEAR ESTIMATION PROCEDURE FOR THE PARAMETERS OF AUTOREGRESSIVE MOVING-AVERAGE PROCESSESJournal of Time Series Analysis, Vol. 12, No. 4 Cross Ref Peak-insensitive parametric spectrum estimationStochastic Processes and their Applications, Vol. 35, No. 1 Cross Ref Review of various approaches to power spectrum estimation Cross Ref Some Problems in the Identification and Estimation of Continuous time Systems from Discrete time Series Cross Ref On Methods for Obtaining Asymptotically Efficient Spectral Parameter Estimates for a Stationary Gaussian Process with Rational Spectral DensityK. O. Dzhaparidze17 July 2006 | Theory of Probability & Its Applications, Vol. 16, No. 3AbstractPDF (560 KB)On the Estimation of the Spectral Parameters of a Gaussian Stationary Process with Rational Spectral DensityK. O. Dzaparidze17 July 2006 | Theory of Probability & Its Applications, Vol. 15, No. 3AbstractPDF (827 KB) Volume 12, Issue 1| 1967Theory of Probability & Its Applications History Submitted:04 August 1965Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1112013Article page range:pp. 115-119ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics