Author | Rao, T. Subba. author |
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Title | An Introduction to Bispectral Analysis and Bilinear Time Series Models [electronic resource] / by T. Subba Rao, M. M. Gabr |
Imprint | New York, NY : Springer US, 1984 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-6318-7 |
Descript | VIII, 280 p. online resource |
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 โ 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