An introduction to bispectral analysis and bilinear time series models (Q796233)

This book is a useful addition to the literature on modeling and forecasting time series. Several results on bispectra and bilinear time- series models are published for the first time in book format. And there is a large number of applications of the theory developed to simulated and real time series data. Chap 1, ''Introduction to stationary time series and spectral analysis'', presents background material on spectral densities and spectral representations of stationary stochastic processes, second-order and higher-order spectra, and spectral properties of linear processes. Chap. 2, ''The estimation of spectral and bispectral density functions'' and Chap. 3, ''Practical bispectral analysis'', discuss the spectral window approach to spectral and bispectral density estimation. An optimum bispectral window is derived and compared in a number of simulated examples with other more or less classical lag windows. Bispectral analysis of some celebrated time series is also reported in chap. 3. Chap. 4, ''Tests for linearity and Gaussianity of stationary time series'', introduces some statistical tests based on bispectra for testing the assumption of linearity and Gaussianity, and illustrates their use with simulated and real data. Chap. 5, ''Bilinear time series'', introduces the bilinear model, derives its Volterra series expansion, its output covariance function, and provides conditions for stationarity and invertibility of such time series models. The problem of estimating the parameters and structure of bilinear models is also discussed in this chapter. Chap. 6, ''Estimation and prediction for subset bilinear time series models with applications'', describes an algorithm for fitting subset bilinear models and illustrates its performances by means of three applications to real time series data. Finally, Chap. 7 is dealing with ''Markovian representations and existence theorems for bilinear time series models''. There are four appendices, the last one containing time series data used for illustration purposes. The book ends with listings of four Fortran programs for fitting the full bilinear model, for estimating the bispectral density function using the optimum window, and for some hypothesis tests based on bispectra.