The Spectral Analysis of Time Series

Probability and Mathematical Statistics
Author: L. H. Koopmans
Publisher: Academic Press
ISBN: 1483218546
Category: Mathematics
Page: 382
View: 3006

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The Spectral Analysis of Time Series describes the techniques and theory of the frequency domain analysis of time series. The book discusses the physical processes and the basic features of models of time series. The central feature of all models is the existence of a spectrum by which the time series is decomposed into a linear combination of sines and cosines. The investigator can used Fourier decompositions or other kinds of spectrals in time series analysis. The text explains the Wiener theory of spectral analysis, the spectral representation for weakly stationary stochastic processes, and the real spectral representation. The book also discusses sampling, aliasing, discrete-time models, linear filters that have general properties with applications to continuous-time processes, and the applications of multivariate spectral models. The text describes finite parameter models, the distribution theory of spectral estimates with applications to statistical inference, as well as sampling properties of spectral estimates, experimental design, and spectral computations. The book is intended either as a textbook or for individual reading for one-semester or two-quarter course for students of time series analysis users. It is also suitable for mathematicians or professors of calculus, statistics, and advanced mathematics.

Spectral Analysis of Time-series Data

Author: Rebecca M. Warner
Publisher: Guilford Press
ISBN: 9781572303386
Category: Social Science
Page: 225
View: 8182

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This book provides a thorough introduction to methods for detecting and describing cyclic patterns in time-series data. It is written both for researchers and students new to the area and for those who have already collected time-series data but wish to learn new ways of understanding and presenting them. Facilitating the interpretation of observations of behavior, physiology, mood, perceptual threshold, social indicator variables, and other responses, the book focuses on practical applications and requires much less mathematical background than most comparable texts. Using real data sets and currently available software (SPSS for Windows), the author employs extensive examples to clarify key concepts. Topics covered include research design issues, preliminary data screening, identification and description of cycles, summary of results across time series, and assessment of relations between time series. Also considered are theoretical questions, problems of interpretation, and potential sources of artifact.

The Spectral Analysis of Time Series

Author: I. G. Žurbenko
Publisher: North Holland
Category: Mathematics
Page: 247
View: 6686

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Examined in this volume are the asymptotic properties of spectral estimates of stationary processes and random fields. A new class of lag window estimates indifferent to remote frequencies is introduced and pseudorandom sequences are investigated from the point of view of their nearness to the sequence of white noise. Principles and algorithms are given for constructing an ideal sequence. A good achievement is the new estimates of higher spectral density asymptotically unbiased and consistent for all admissible values of the argument. A new type of the random number generator which is sufficiently close to white noise is introduced.

Singular Spectrum Analysis

A New Tool in Time Series Analysis
Author: J.B. Elsner,A.A. Tsonis
Publisher: Springer Science & Business Media
ISBN: 9780306454721
Category: Business & Economics
Page: 164
View: 1056

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This original new text provides an easily accessible introduction to this important new topic in time series analysis. The authors emphasize examples over theoretical explanations and the need for proper and careful statistical tests in the context of data exploration. The book's focus is on the application of the method in signal detection, filtering, and prediction. Instructors and students will appreciate the step-by-step presentation of underlying ideas.

Modern Spectrum Analysis of Time Series

Fast Algorithms and Error Control Techniques
Author: Prabhakar S. Naidu
Publisher: CRC Press
ISBN: 9780849324642
Category: Mathematics
Page: 416
View: 941

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Spectrum analysis can be considered as a topic in statistics as well as a topic in digital signal processing (DSP). This book takes a middle course by emphasizing the time series models and their impact on spectrum analysis. The text begins with elements of probability theory and goes on to introduce the theory of stationary stochastic processes. The depth of coverage is extensive. Many topics of concern to spectral characterization of Gaussian and non-Gaussian time series, scalar and vector time series are covered. A section is devoted to the emerging areas of non-stationary and cyclostationary time series. The book is organized more as a textbook than a reference book. Each chapter includes many examples to illustrate the concepts described. Several exercises are included at the end of each chapter. The level is appropriate for graduate and research students.

Fourier Analysis of Time Series

An Introduction
Author: Peter Bloomfield
Publisher: John Wiley & Sons
ISBN: 0471653993
Category: Mathematics
Page: 288
View: 3345

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A new, revised edition of a yet unrivaled work on frequencydomain analysis Long recognized for his unique focus on frequency domain methodsfor the analysis of time series data as well as for his applied,easy-to-understand approach, Peter Bloomfield brings his well-known1976 work thoroughly up to date. With a minimum of mathematics andan engaging, highly rewarding style, Bloomfield provides in-depthdiscussions of harmonic regression, harmonic analysis, complexdemodulation, and spectrum analysis. All methods are clearlyillustrated using examples of specific data sets, while ampleexercises acquaint readers with Fourier analysis and itsapplications. The Second Edition: Devotes an entire chapter to complex demodulation Treats harmonic regression in two separate chapters Features a more succinct discussion of the fast Fouriertransform Uses S-PLUS commands (replacing FORTRAN) to accommodateprogramming needs and graphic flexibility Includes Web addresses for all time series data used in theexamples An invaluable reference for statisticians seeking to expandtheir understanding of frequency domain methods, FourierAnalysis of Time Series, Second Edition also provides easyaccess to sophisticated statistical tools for scientists andprofessionals in such areas as atmospheric science, oceanography,climatology, and biology.

The Statistical Analysis of Time Series

Author: Theodore W. Anderson
Publisher: John Wiley & Sons
ISBN: 1118150392
Category: Mathematics
Page: 704
View: 2638

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The Wiley Classics Library consists of selected books that havebecome recognized classics in their respective fields. With thesenew unabridged and inexpensive editions, Wiley hopes to extend thelife of these important works by making them available to futuregenerations of mathematicians and scientists. Currently availablein the Series: T. W. Anderson Statistical Analysis of Time SeriesT. S. Arthanari & Yadolah Dodge Mathematical Programming inStatistics Emil Artin Geometric Algebra Norman T. J. Bailey TheElements of Stochastic Processes with Applications to the NaturalSciences George E. P. Box & George C. Tiao Bayesian Inferencein Statistical Analysis R. W. Carter Simple Groups of Lie TypeWilliam G. Cochran & Gertrude M. Cox Experimental Designs,Second Edition Richard Courant Differential and Integral Calculus,Volume I Richard Courant Differential and Integral Calculus, VolumeII Richard Courant & D. Hilbert Methods of MathematicalPhysics, Volume I Richard Courant & D. Hilbert Methods ofMathematical Physics, Volume II D. R. Cox Planning of ExperimentsHarold M. S. Coxeter Introduction to Modern Geometry, SecondEdition Charles W. Curtis & Irving Reiner Representation Theoryof Finite Groups and Associative Algebras Charles W. Curtis &Irving Reiner Methods of Representation Theory with Applications toFinite Groups and Orders, Volume I Charles W. Curtis & IrvingReiner Methods of Representation Theory with Applications to FiniteGroups and Orders, Volume II Bruno de Finetti Theory ofProbability, Volume 1 Bruno de Finetti Theory of Probability,Volume 2 W. Edwards Deming Sample Design in Business Research Amosde Shalit & Herman Feshbach Theoretical Nuclear Physics, Volume1 --Nuclear Structure J. L. Doob Stochastic Processes NelsonDunford & Jacob T. Schwartz Linear Operators, Part One, GeneralTheory Nelson Dunford & Jacob T. Schwartz Linear Operators,Part Two, Spectral Theory--Self Adjoint Operators in Hilbert SpaceNelson Dunford & Jacob T. Schwartz Linear Operators, PartThree, Spectral Operators Herman Fsehbach Theoretical NuclearPhysics: Nuclear Reactions Bernard Friedman Lectures onApplications-Oriented Mathematics Gerald d. Hahn & Samuel S.Shapiro Statistical Models in Engineering Morris H. Hansen, WilliamN. Hurwitz & William G. Madow Sample Survey Methods and Theory,Volume I--Methods and Applications Morris H. Hansen, William N.Hurwitz & William G. Madow Sample Survey Methods and Theory,Volume II--Theory Peter Henrici Applied and Computational ComplexAnalysis, Volume 1--Power Series--lntegration--ConformalMapping--Location of Zeros Peter Henrici Applied and ComputationalComplex Analysis, Volume 2--Special Functions--IntegralTransforms--Asymptotics--Continued Fractions Peter Henrici Appliedand Computational Complex Analysis, Volume 3--Discrete FourierAnalysis--Cauchy Integrals--Construction of ConformalMaps--Univalent Functions Peter Hilton & Yel-Chiang Wu A Coursein Modern Algebra Harry Hochetadt Integral Equations Erwin O.Kreyezig Introductory Functional Analysis with Applications WilliamH. Louisell Quantum Statistical Properties of Radiation All HasanNayfeh Introduction to Perturbation Techniques Emanuel ParzenModern Probability Theory and Its Applications P.M. Prenter Splinesand Variational Methods Walter Rudin Fourier Analysis on Groups C.L. Siegel Topics in Complex Function Theory, Volume I--EllipticFunctions and Uniformization Theory C. L. Siegel Topics in ComplexFunction Theory, Volume II--Automorphic and Abelian integrals C. LSiegel Topics in Complex Function Theory, Volume III--AbelianFunctions & Modular Functions of Several Variables J. J. StokerDifferential Geometry J. J. Stoker Water Waves: The MathematicalTheory with Applications J. J. Stoker Nonlinear Vibrations inMechanical and Electrical Systems

Introduction to Time Series and Forecasting

Author: Peter J. Brockwell,Richard A. Davis,R. J. Davis
Publisher: Taylor & Francis
ISBN: 9780387953519
Category: Business & Economics
Page: 434
View: 1724

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This is an introduction to time series that emphasizes methods and analysis of data sets. The logic and tools of model-building for stationary and non-stationary time series are developed and numerous exercises, many of which make use of the included computer package, provide the reader with ample opportunity to develop skills. Statisticians and students will learn the latest methods in time series and forecasting, along with modern computational models and algorithms.

Elements of Multivariate Time Series Analysis

Author: Gregory C. Reinsel
Publisher: Springer Science & Business Media
ISBN: 9780387406190
Category: Mathematics
Page: 358
View: 1279

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This text concentrates on the time-domain analysis of multivariate time series, and assumes a background in univariate time series analysis. It also includes exercise sets and multivariate time series data sets. The book should also be useful to researchers and graduate students in the areas of statistics, econometrics, business, and engineering.

Developments in Time Series Analysis

Author: T. Subba Rao
Publisher: CRC Press
ISBN: 9780412492600
Category: Mathematics
Page: 440
View: 6388

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This volume contains 27 papers, written by time series analysts, dealing with statistical theory, methodology and applications. The emphasis is on the recent developments in the analysis of linear, onlinear (non-Gaussian), stationary and nonstationary time series. The topics include cointegration, estimation and asymptotic theory, Kalman filtering, nonparametric statistical inference, long memory models, nonlinear models, spectral analysis of stationary and nonstationary processes. Quite a number of papers are devoted to modelling and analysis of real time series, and the econometricians, mathematical statisticians, communications engineers and scientists who use time series techniques and Fourier analysis should find the papers in this volume useful.

Smoothness Priors Analysis of Time Series

Author: Genshiro Kitagawa,Will Gersch
Publisher: Springer Science & Business Media
ISBN: 1461207614
Category: Mathematics
Page: 280
View: 8668

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Smoothness Priors Analysis of Time Series addresses some of the problems of modeling stationary and nonstationary time series primarily from a Bayesian stochastic regression "smoothness priors" state space point of view. Prior distributions on model coefficients are parametrized by hyperparameters. Maximizing the likelihood of a small number of hyperparameters permits the robust modeling of a time series with relatively complex structure and a very large number of implicitly inferred parameters. The critical statistical ideas in smoothness priors are the likelihood of the Bayesian model and the use of likelihood as a measure of the goodness of fit of the model. The emphasis is on a general state space approach in which the recursive conditional distributions for prediction, filtering, and smoothing are realized using a variety of nonstandard methods including numerical integration, a Gaussian mixture distribution-two filter smoothing formula, and a Monte Carlo "particle-path tracing" method in which the distributions are approximated by many realizations. The methods are applicable for modeling time series with complex structures.

Unterrichtsentwürfe Mathematik Primarstufe

Author: Kirsten Heckmann,Friedhelm Padberg
Publisher: Springer-Verlag
ISBN: 364239745X
Category: Mathematics
Page: 355
View: 453

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Dieses Buch bietet vielseitige, innovative und dennoch praktikable Anregungen für die Planung und Realisierung ihres Mathematikunterrichts in der Primarstufe – einschließlich reichhaltiger Arbeitsmaterialien. Die theoretischen Grundlagen zu den Prinzipien des heutigen Mathematikunterrichts sowie zur Planung und Gestaltung von Unterricht im ersten Teil dieses Bandes erfahren eine praktische Umsetzung durch 20 authentische, sorgfältig ausgesuchte Unterrichtsentwürfe, die das Herzstück dieses Buches bilden. Die Hälfte dieser Unterrichtsentwürfe sind Entwürfe für Examenslehrproben, die andere Hälfte ebenfalls besonders gut gelungene Entwürfe. Die Unterrichtsentwürfe spiegeln die aktuellen Anforderungen und Zielsetzungen des Mathematikunterrichts der Primarstufe gut wider. Sie decken nämlich weitestgehend die prozessbezogenen und inhaltsbezogenen mathematischen Kompetenzen/Leitideen der neuesten Kernlehrpläne/Bildungsstandards ab. Ferner lassen sich die Planungen relativ leicht auf viele andere Unterrichtsstunden übertragen.

Time Series: Theory and Methods

Author: Peter J. Brockwell,Richard A. Davis
Publisher: Springer Science & Business Media
ISBN: 1441903194
Category: Business & Economics
Page: 577
View: 2742

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This paperback edition is a reprint of the 1991 edition. Time Series: Theory and Methods is a systematic account of linear time series models and their application to the modeling and prediction of data collected sequentially in time. The aim is to provide specific techniques for handling data and at the same time to provide a thorough understanding of the mathematical basis for the techniques. Both time and frequency domain methods are discussed, but the book is written in such a way that either approach could be emphasized. The book is intended to be a text for graduate students in statistics, mathematics, engineering, and the natural or social sciences. It contains substantial chapters on multivariate series and state-space models (including applications of the Kalman recursions to missing-value problems) and shorter accounts of special topics including long-range dependence, infinite variance processes, and nonlinear models. Most of the programs used in the book are available in the modeling package ITSM2000, the student version of which can be downloaded from