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An Introduction to Bispectral Analysis and Bilinear Time Series Models

  • T. Subba Rao
  • M. M. Gabr

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

Table of contents

  1. Front Matter
    Pages I-VIII
  2. T. Subba Rao, M. M. Gabr
    Pages 65-115
  3. T. Subba Rao, M. M. Gabr
    Pages 116-144
  4. T. Subba Rao, M. M. Gabr
    Pages 145-187
  5. Back Matter
    Pages 230-280

About this book

Introduction

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.

Keywords

Analysis Bilineares Modell Fitting Random variable Series Spektralanalyse Time Time series Variance Zeitreihenanalyse best fit

Authors and affiliations

  • T. Subba Rao
    • 1
  • M. M. Gabr
    • 2
  1. 1.Department of MathematicsUniversity of ManchesterManchesterEngland
  2. 2.Department of MathematicsUniversity of AlexandriaAlexandriaEgypt

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-6318-7
  • Copyright Information Springer-Verlag New York 1984
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-96039-5
  • Online ISBN 978-1-4684-6318-7
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site
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