Time Series in the Frequency Domain

Edited by

  • D.R. Brillinger
  • P.R. Krishnaiah

This volume of the Handbook is concerned particularly with the frequency side, or spectrum, approach to time series analysis. This approach involves essential use of sinusoids and bands of (angular) frequency, with Fourier transforms playing an important role. A principal activity is thinking of systems, their inputs, outputs, and behavior in sinusoidal terms. In many cases, the frequency side approach turns out to be simpler with respect to computational, mathematical, and statistical aspects. In the frequency approach, an assumption of stationarity is commonly made. However, the essential roles played by the techniques of complex demodulation and seasonal adjustment show that stationarity is far from being a necessary condition. Assumptions of Gaussianity and linearity are also commonly made and yet, as a variety of the papers illustrate, these assumptions are not necessary. This volume complements Handbook of Statistics 5: Time Series in the Time Domain.
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Book information

  • Published: February 1984
  • Imprint: ELSEVIER
  • ISBN: 978-0-444-86726-1


This book is definitely one that should be included in any statistics library.
Journal of the American Statistical Association

Table of Contents

Wiener Filtering (with Emphasis on Frequency-Domain Approaches) (R.J. Bhansali, D. Karavellas). The Finite Fourier Transform of a Stationary Process (D.R. Brillinger). Seasonal and Calendar Adjustment (W.S. Cleveland). Optimal Inference in the Frequency Domain (R.B. Davies). Applications of Spectral Analysis in Econometrics (C.W.J. Granger, R. Engle). Signal Estimation (E.J. Hannan). Complex Demodulation: Some Theory and Applications (T. Hasan). Estimating the Gain of a Linear Filter from Noisy Data (M.J. Hinich). A Spectral Analysis Primer (L.H. Koopmans). Robust-Resistant Spectral Analysis (R.D. Martin). Autoregressive Spectral Estimation (E. Parzen). Threshold Autoregression and some Frequency-Domain Characteristics (J. Pemberton, H. Tong). The Frequency Domain Approach to the Analysis of Closed-Loop Systems (M.B. Priestley). The Bispectral Analysis of Nonlinear Stationary Time Series with Reference to Bilinear-Time Series Models (T.S. Rao). Frequency-Domain Analysis of Multidimensional Time-Series Data (E.A. Robinson). Review of Various Approaches to Power Spectrum Estimation (P.M. Robinson). Cumulant and Cumulant Spectra (M. Rosenblatt). Replicated Time Series Regression: An Approach to Signal Estimation and Detection (R.H. Shumway). Computer Programming of Spectrum Estimation (T. Thrall). Likelihood Ratio Tests on Covariance Matrices and Mean Vectors of Complex Multivariate Normal Populations and their Applications in Time Series (P.R. Krishnaiah, J.C. Lee, T.C. Chang).