An introduction to bispectral analysis and bilinear time series models

T. Subba Rao, M.M. Gabr


  • 1 Introduction to Stationary time Series and Spectral Analysis.- 1.1 Some basic Definitions.- 1.2 Spectral Densities and Spectral Representations.- 1.3 Higher Order Spectra (Polyspectra).- 1.4 Bispectral Density Functions.- 1.5 Standard Linear Models - their spectra and bispectra.- 1.6 State Space Representation of Linear Time Series Models.- 1.7 Bispectra and Linear Processes.- 1.8 Invertibility of Time Series Models.- 2 The Estimation of Spectral and Bispectral Density Functions.- 2.1 Introduction.- 2.2 Estimation of the Spectral Density Function.- 2.3 Estimation of the Bispectral Density Function.- 2.4 Optimum Bispectral Window.- 2.5 Comparison of Bispectral Lag Windows.- 2.6 Bispectral Density Function of BL(1,0,1,1) Model.- 3 Practical Bispectral Analysis.- 3.1 The Choice of Truncation Point (M).- 3.2 Comparison of Parametric and Non-Parameteric Bispectral Estimates.- 3.3 Bispectral Analysis of some Time Series Data.- 3.4 Some Nonlinear Phenomena.- 4 Tests for Linearity and Gaussianity of Stationary time Series.- 4.1 General Introduction.- 4.2 Spectrum and Bispectrum of Linear Processes.- 4.3 Test for Symmetry and Linearity.- 4.4 Test for Linearity.- 4.5 Choice of Parameters.- 4.6 Numerical Illustrations.- 4.7 Applications to Real Time Series.- 5 Bilinear time Series Models.- 5.1 Non-Linear Representations in terms of independent random variables.- 5.2 Bilinear Time Series Models.- 5.3 Volterra Series Expansion of YBL(p) Models.- 5.4 Expressions for Covariances and Conditions for Stationarity.- 5.5 Invertibility of the VBL(p) Model.- 5.6 Conditions for Stationarity of the Diagonal Bilinear Model, DBL(?).- 5.7 Conditions for Stationarity of the Lower Triangular Bilinear Model, LTBL (?,?).- 5.8 Estimation of the Parameters of Bilinear Models.- 5.9 Determination of the Order of Bilinear Models.- 5.10 Numerical Illustrations.- 5.11 Sampling Properties of Parameter Estimations for the BL(1,0,1,1) Model.- 6 Estimation and Prediction for Subset Bilinear time Series Models with Applications.- 6.1 Introduction.- 6.2 An Algorithm for Fitting Subset Bilinear Models.- 6.3 Estimation of the Parameters of SBL(k?,m).- 6.4 Residuals.- 6.5 Fitting Subset Bilinear Models to Time Series Data.- 7 Markovian Representation and Existence Theorems for Bilinear time Series Models.- 7.1 Markovian Representations.- 7.2 Existence of the Bilinear Model BL(p,0,p,1).- Appendix A On the Kronecker Matrix Product.- Appendix B Linear Least Squares Solutions by Householder Transformations.- Appendix C Fitting the Best AR Model.- Appendix D Time Series Data.- Listing of Programs.- Program 1.- Program 2.- Program 3.- Program 4.- References.- Author Index.

「Nielsen BookData」より


書名 An introduction to bispectral analysis and bilinear time series models
著作者等 Subba Rao, T
Gabr, M. M.
Rao T.S.
シリーズ名 Lecture notes in statistics
出版元 Springer-Verlag
刊行年月 1984
版表示 Softcover reprint of the original 1st ed. 1984
ページ数 vi, 280 p.
大きさ 25 cm
ISBN 3540960392
NCID BA01442562
※クリックでCiNii Booksを表示
言語 英語
出版国 アメリカ合衆国

Clip to Evernote