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An Introduction to Bispectral Analysis and Bilinear Time Series Models

  • Book
  • © 1984

Overview

Authors:
  1. T. Subba Rao

    1. Department of Mathematics, University of Manchester, Manchester, England

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    You can also search for this author in PubMed   Google Scholar

  2. M. M. Gabr

    1. Department of Mathematics, University of Alexandria, Alexandria, Egypt

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Statistics (LNS, volume 24)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Introduction to Stationary Time Series and Spectral Analysis

    • T. Subba Rao, M. M. Gabr
    Pages 1-28

  3. The Estimation of Spectral and Bispectral Density Functions

    • T. Subba Rao, M. M. Gabr
    Pages 29-64

  4. Practical Bispectral Analysis

    • T. Subba Rao, M. M. Gabr
    Pages 65-115

  5. Tests for Linearity and Gaussianity of Stationary Time Series

    • T. Subba Rao, M. M. Gabr
    Pages 116-144

  6. Bilinear Time Series Models

    • T. Subba Rao, M. M. Gabr
    Pages 145-187

  7. Estimation and Prediction for Subset Bilinear Time Series Models with Applications

    • T. Subba Rao, M. M. Gabr
    Pages 188-215

  8. Markovian Representation and Existence Theorems for Bilinear Time Series Models

    • T. Subba Rao, M. M. Gabr
    Pages 216-229

  9. Back Matter

    Pages 230-280
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Keywords

About this book

The theory of time series models has been well developed over the last thirt,y years. Both the frequenc.y domain and time domain approaches have been widely used in the analysis of linear time series models. However. many physical phenomena cannot be adequately represented by linear models; hence the necessity of nonlinear models and higher order spectra. Recently a number of nonlinear models have been proposed. In this monograph we restrict attention to one particular nonlinear model. known as the "bilinear model". The most interesting feature of such a model is that its second order covariance analysis is ve~ similar to that for a linear model. This demonstrates the importance of higher order covariance analysis for nonlinear models. For bilinear models it is also possible to obtain analytic expressions for covariances. spectra. etc. which are often difficult to obtain for other proposed nonlinear models. Estimation of bispectrum and its use in the construction of tests for linearit,y and symmetry are also discussed. All the methods are illustrated with simulated and real data. The first author would like to acknowledge the benefit he received in the preparation of this monograph from delivering a series of lectures on the topic of bilinear models at the University of Bielefeld. Ecole Normale Superieure. University of Paris (South) and the Mathematisch Cen trum. Ams terdam.

Authors and Affiliations

  • Department of Mathematics, University of Manchester, Manchester, England

    T. Subba Rao

  • Department of Mathematics, University of Alexandria, Alexandria, Egypt

    M. M. Gabr

Bibliographic Information

  • Book Title: An Introduction to Bispectral Analysis and Bilinear Time Series Models

  • Authors: T. Subba Rao, M. M. Gabr

  • Series Title: Lecture Notes in Statistics

  • DOI: https://doi.org/10.1007/978-1-4684-6318-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1984

  • Softcover ISBN: 978-0-387-96039-5Published: 05 September 1984

  • eBook ISBN: 978-1-4684-6318-7Published: 06 December 2012

  • Series ISSN: 0930-0325

  • Series E-ISSN: 2197-7186

  • Edition Number: 1

  • Number of Pages: VIII, 280

  • Topics: Probability Theory and Stochastic Processes, Applications of Mathematics

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