The Spectral Analysis Of Time Series

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.

To tailor time series models to a particular physical problem and to follow the working of various techniques for processing and analyzing data, one must understand the basic theory of spectral (frequency domain) analysis of time series. This classic book provides an introduction to the techniques and theories of spectral analysis of time series. In a discursive style, and with minimal dependence on mathematics, the book presents the geometric structure of spectral analysis. This approach makes possible useful, intuitive interpretations of important time series parameters and provides a unified framework for an otherwise scattered collection of seemingly isolated results. The books strength lies in its applicability to the needs of readers from many disciplines with varying backgrounds in mathematics. It provides a solid foundation in spectral analysis for fields that include statistics, signal process engineering, economics, geophysics, physics, and geology. Appendices provide details and proofs for those who are advanced in math. Theories are followed by examples and applications over a wide range of topics such as meteorology, seismology, and telecommunications. Topics covered include Hilbert spaces; univariate models for spectral analysis; multivariate spectral models; sampling, aliasing, and discrete-time models; real-time filtering; digital filters; linear filters; distribution theory; sampling properties ofspectral estimates; and linear prediction. Hilbert spaces univariate models for spectral analysis multivariate spectral models sampling, aliasing, and discrete-time models real-time filtering digital filters linear filters distribution theory sampling properties of spectral estimates linear prediction

The Spectral Analysis of Time Series ...

Singular spectrum analysis (SSA) is a technique of time series analysis and forecasting combining elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing. SSA seeks to decompose the original series into a sum of a small number of interpretable components such as trend, oscillatory components and noise. It is based on the singular value decomposition of a specific matrix constructed upon the time series. Neither a parametric model nor stationarity are assumed for the time series. This makes SSA a model-free method and hence enables SSA to have a very wide range of applicability. The present book is devoted to the methodology of SSA and shows how to use SSA both safely and with maximum effect. Potential readers of the book include: professional statisticians and econometricians, specialists in any discipline in which problems of time series analysis and forecasting occur, specialists in signal processing and those needed to extract signals from noisy data, and students taking courses on applied time series analysis.

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.

Spectral analysis is widely used to interpret time series collected in diverse areas. This book covers the statistical theory behind spectral analysis and provides data analysts with the tools needed to transition theory into practice. Actual time series from oceanography, metrology, atmospheric science and other areas are used in running examples throughout, to allow clear comparison of how the various methods address questions of interest. All major nonparametric and parametric spectral analysis techniques are discussed, with emphasis on the multitaper method, both in its original formulation involving Slepian tapers and in a popular alternative using sinusoidal tapers. The authors take a unified approach to quantifying the bandwidth of different nonparametric spectral estimates. An extensive set of exercises allows readers to test their understanding of theory and practical analysis. The time series used as examples and R language code for recreating the analyses of the series are available from the book's website.

. . ) (under the assumption that the spectral density exists). For this reason, a vast amount of periodical and monographic literature is devoted to the nonparametric statistical problem of estimating the function tJ( T) and especially that of leA) (see, for example, the books [4,21,22,26,56,77,137,139,140,]). However, the empirical value t;; of the spectral density I obtained by applying a certain statistical procedure to the observed values of the variables Xl' . . . , X , usually depends in n a complicated manner on the cyclic frequency). . This fact often presents difficulties in applying the obtained estimate t;; of the function I to the solution of specific problems rela ted to the process X . Theref ore, in practice, the t obtained values of the estimator t;; (or an estimator of the covariance function tJ~( T» are almost always "smoothed," i. e. , are approximated by values of a certain sufficiently simple function 1 = 1

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.