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(1011) 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. 9Determination of the Order of Bilinear Models. - 5. 10 Numerical Illustrations. - 5. 11 Sampling Properties of Parameter Estimations for the BL(1011) 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(p0p1). - 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. Language: English