A new approach to bilinear time series estimation

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In the first part of chapter 2 we motivate the bilinear approach to nonlinear time series not only in a theoretical way but also by means of some simulations of the simple bilinear process. In a second part then the book show how the method of CLS can be applied to the estimation of bilinear models and the special problems which arise in estimating this kind of nonlinear models. The third part consists of the definition of standardized bilinear time series and some related remarks. In the last section of the chapter the basic notations are summarized. In chapter 3 conditional convariance structure of general standardized superdiagonal bilinear time series is study. In Chapter 4 conditional covariances into account to define the CLS estimation procedure applied to two bilinear models are considered. Chapter 5 contains the theoretical results which are attainable for the estimators suggested in chapter 4.