An Introduction to Bispectral Analysis and Bilinear Time Series Models.

作者：G. Janacek, T. SUBBA RAO, M. M. Gabr · 发表于：Journal of the Royal Statistical Society Series A (General) · 年份：1987 · DOI：10.2307/2981645 · 被引用次数：464 · 研究领域：Spectroscopy and Chemometric Analyses、Neural Networks and Applications

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 Condi...