The Spectral Analysis of Time Series

Probability and Mathematical Statistics
Author: L. H. Koopmans
Publisher: Academic Press
ISBN: 1483218546
Category: Mathematics
Page: 382
View: 7411

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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: 6919

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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
ISBN: N.A
Category: Mathematics
Page: 247
View: 2899

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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: 1475725140
Category: Business & Economics
Page: 164
View: 7174

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The term singular spectrum comes from the spectral (eigenvalue) decomposition of a matrix A into its set (spectrum) of eigenvalues. These eigenvalues, A, are the numbers that make the matrix A -AI singular. The term singular spectrum analysis· is unfortunate since the traditional eigenvalue decomposition involving multivariate data is also an analysis of the singular spectrum. More properly, singular spectrum analysis (SSA) should be called the analysis of time series using the singular spectrum. Spectral decomposition of matrices is fundamental to much the ory of linear algebra and it has many applications to problems in the natural and related sciences. Its widespread use as a tool for time series analysis is fairly recent, however, emerging to a large extent from applications of dynamical systems theory (sometimes called chaos theory). SSA was introduced into chaos theory by Fraedrich (1986) and Broomhead and King (l986a). Prior to this, SSA was used in biological oceanography by Colebrook (1978). In the digi tal signal processing community, the approach is also known as the Karhunen-Loeve (K-L) expansion (Pike et aI., 1984). Like other techniques based on spectral decomposition, SSA is attractive in that it holds a promise for a reduction in the dimen- • Singular spectrum analysis is sometimes called singular systems analysis or singular spectrum approach. vii viii Preface sionality. This reduction in dimensionality is often accompanied by a simpler explanation of the underlying physics.

Automatic Autocorrelation and Spectral Analysis


Author: Petrus M.T. Broersen
Publisher: Springer Science & Business Media
ISBN: 1846283299
Category: Technology & Engineering
Page: 298
View: 2780

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Spectral analysis requires subjective decisions which influence the final estimate and mean that different analysts can obtain different results from the same stationary stochastic observations. Statistical signal processing can overcome this difficulty, producing a unique solution for any set of observations but that is only acceptable if it is close to the best attainable accuracy for most types of stationary data. This book describes a method which fulfils the above near-optimal-solution criterion, taking advantage of greater computing power and robust algorithms to produce enough candidate models to be sure of providing a suitable candidate for given data.

Fourier Analysis of Time Series

An Introduction
Author: Peter Bloomfield
Publisher: John Wiley & Sons
ISBN: 0471653993
Category: Mathematics
Page: 288
View: 633

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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.

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: 7825

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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.

Spectral Analysis of Economic Time Series. (PSME-1)


Author: Clive William John Granger,Michio Hatanaka
Publisher: Princeton University Press
ISBN: 1400875528
Category: Business & Economics
Page: 318
View: 5373

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The important data of economics are in the form of time series; therefore, the statistical methods used will have to be those designed for time series data. New methods for analyzing series containing no trends have been developed by communication engineering, and much recent research has been devoted to adapting and extending these methods so that they will be suitable for use with economic series. This book presents the important results of this research and further advances the application of the recently developed Theory of Spectra to economics. In particular, Professor Hatanaka demonstrates the new technique in treating two problems-business cycle indicators, and the acceleration principle existing in department store data. Originally published in 1964. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Developments in Time Series Analysis


Author: T. Subba Rao
Publisher: CRC Press
ISBN: 9780412492600
Category: Mathematics
Page: 440
View: 7676

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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.

Digital Spectral Analysis

Parametric, Non-Parametric and Advanced Methods
Author: Francis Castanié
Publisher: John Wiley & Sons
ISBN: 1118601831
Category: Mathematics
Page: 400
View: 1184

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Digital Spectral Analysis provides a single source thatoffers complete coverage of the spectral analysis domain. Thisself-contained work includes details on advanced topics that areusually presented in scattered sources throughout theliterature. The theoretical principles necessary for the understanding ofspectral analysis are discussed in the first four chapters:fundamentals, digital signal processing, estimation in spectralanalysis, and time-series models. An entire chapter is devoted to the non-parametric methods mostwidely used in industry. High resolution methods are detailed in a further four chapters:spectral analysis by stationary time series modeling, minimumvariance, and subspace-based estimators. Finally, advanced concepts are the core of the last four chapters:spectral analysis of non-stationary random signals, space timeadaptive processing: irregularly sampled data processing, particlefiltering and tracking of varying sinusoids. Suitable for students, engineers working in industry, and academicsat any level, this book provides a rare complete overview of thespectral analysis domain.

A Handbook of Time-series Analysis, Signal Processing and Dynamics


Author: D. S. G. Pollock
Publisher: Academic Press
ISBN: 9780125609906
Category: Technology & Engineering
Page: 733
View: 1950

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The aim of this book is to serve as a graduate text and reference in time series analysis and signal processing, two closely related subjects that are the concern of a wide range of disciplines, such as statistics, electrical engineering, mechanical engineering and physics. The book provides a CD-ROM containing codes in PASCAL and C for the computer procedures printed in the book. It also furnishes a complete program devoted to the statistical analysis of time series, which will be attractive to a wide range of academics working in diverse mathematical disciplines.

The Statistical Analysis of Time Series


Author: Theodore W. Anderson
Publisher: John Wiley & Sons
ISBN: 1118150392
Category: Mathematics
Page: 704
View: 5397

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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