The Spectral Analysis of Time Series

The Spectral Analysis of Time Series

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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 frequency domain (spectral) analysis of time series. This book provides an introduction to the techniques and theories of spectral analysis of time series. 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 of results. The book should be useful to the needs of readers from many disciplines with varying degrees of preparation in mathematics. It provides a solid background in spectral analysis for fields that include statistics signal process engineering, economics, geophysics, physics and geology. Appendices, the end of each chapter provide details and proofs for those who are advanced in maths. Theories are followed by examples and applications in a wide range of topics such as me orology, seismology and telecommunications.
Topics covered include: Hilbert Spaces; univariate models for spectral analysis; multi-variate spectral models; sampling, aliasing and discrete-time models; real-time filtering; digital filters; linear filters; distribution theory; sampling properties of spectral estimates; and linear prediction.
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Product details

  • Paperback | 366 pages
  • 152.4 x 226.06 x 20.32mm | 1,428.81g
  • Academic Press Inc
  • San Diego, United States
  • English
  • New edition
  • New edition
  • references, indices
  • 0124192513
  • 9780124192515

Table of contents

Preliminaries: Time Series and Spectra, Summary of Vector Space Geometry, Some Probability Notations and Properties. Models for Spectral Analysis - The Univariate Case: The Wiener Theory of Spectral Analysis, Stationary and Weakly Stationary Stochastic Processes, The Spectral Representation for Weakly Stationary Stochastic Processes - A Special Case, The General Spectral Representation for Weakly Stationary Processes, The Discrete and Continuous Components of the Process, Physical Realizations of the Different Kinds of Spectra, The Real Spectral Representation, Ergodicity and the Connection between the Wiener and Stationary Process Theories, Statistical Estimation of the Autocovariance and the Mean Ergodic Theorem. Sampling, Aliasing, and Discrete-Time Models: Sampling and the Aliasing Problem, The Spectral Model for Discrete-Time Series; Linear Filters - General Properties with Applications to Continuous-Time Processes: Linear Filters, Combining Linear Filters, Inverting Linear Filters, Nonstationary Processes Generated by Time Varying Linear Filters. Multivariate Spectral Models and Their Applications: The Spectrum of a Multivariate Time Series-Wiener Theory, Multivariate Weakly Stationary Stochastic Processes, Linear Filters for Multivariate Time Series, The Bivariate Spectral Parameters, Their Interpretations and Uses. The Multivariate Spectral Parameters, Their Interpretations and Uses; Digital Filters: General Properties of Digital Filters, The Effect of Finite Data Length, Digital Filters with Finitely Many Nonzero Weights, Digital Filters Obtained by Combining Simple Filters, Filters with Gapped Weights and Results Concerning the Filtering of Series with Polynomial Trends. Finite Parameter Models, Linear Prediction and Real-Time Filtering: Moving Averages, Autoregressive Processes, The Linear Prediction Problem, Mixed Autoregressive-Moving Average Processes and Recursive Prediction, Linear Filtering in Real Time. The Distribution Theory of Spectral Estimates with Applications to Statistical Inference: Distribution of the Finite Fourier Transform and the Periodogram. Distribution Theory for Univariate Spectral Estimators, Distribution Theory for Multivariate Spectral Estimators with Applications to Statistical Inference. Sampling Properties of Spectral Estimates, Experimental Design and Spectral Computations, Properties of Spectral Estimators and the Selection of Spectral Windows, Experimental Design, Methods for Computing Spectral Estimators, Data Processing Problems and Techniques.
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