The Spectral Analysis of Time SeriesTo 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 discretetime models; realtime filtering; digital filters; linear filters; distribution theory; sampling properties ofspectral estimates; and linear prediction.

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Contents
1  
29  
Chapter 3 Sampling Aliasing and DiscreteTime Models  66 
Chapter 4 Linear FiltersGeneral Properties with Applications to ContinuousTime Processes  79 
Chapter 5 Multivariate Spectral Models and Their Applications  119 
Chapter 6 Digital Filters  165 
Chapter 7 Finite Parameter Models Linear Prediction and RealTime Filtering  210 
Chapter 8 The Distribution Theory of Spectral Estimates with Applications to Statistical Inference  257 
Chapter 9 Sampling Properties of Spectral Estimates Experimental Design and Spectral Computations  294 
354  
359  
Probability and Mathematical Statistics  367 
Other editions  View all
The Spectral Analysis of Time Series: Probability and ..., Volume 22 L. H. Koopmans Limited preview  2014 
Common terms and phrases
applications asymptotic autoregression bandpass filters bandwidth calculate Chapter coefficient of coherence complex complexvalued components computed condition confidence interval Consequently continuous spectrum continuoustime convolution filter defined degrees of freedom denote determined digital filter discrete discussion equation equivalent example expression fast Fourier transform filter with transfer follows Fourier series frequency graph Hannan Hilbert space important inner product input integral lag window linear filter linear subspace lowpass filter matrix method Moreover moving average moving average representation multivariate obtain onesided moving average operations output peaks periodic function polynomial prediction predictor problem properties random variables realvalued regression sample satisfy sequence series analysis side lobes smoothed periodogram estimator spectral density function spectral distribution spectral estimators spectral parameters spectral representation spectral window spectrum analysis symmetric tapering theorem theory transfer function transfer function B(A uncorrelated values variance vector weakly stationary process weighted covariance estimator white noise white noise process zero