The Parameter Estimation Of Bilinear Time Series Model

Parameter estimation is the most important in the research on Time Series Analysis. There are many methods to estimate parameters in linear time analysis model. Bilinear model is a kind of nonlinear model. It is in the simple form and to some extent a linear model. Just because of the bilinear item in the model, it is not always effective to estimate parameters in the bilinear model with the methods we generally use in parameter estimation.Several methods are mentioned in the article to estimate parameters in the BL(P,0,1,1) model, as well as the statistical personalities.Firstly, it is presented the basic introduction on general bilinear model, stable conditions, and covariance. Secondly, the stationary and the reversible condition of the BL(P,0,1,1) model are described. On the stationary condition, we estimate parameters in the BL(P,0,1,1) model with the method of moment estimation, Recursive prediction error estimation, Least squares estimation, and Optimal filtering method. And the related statistical personalities are discussed. Thirdly, traditional Linear model prediction theory is used to study the Conditional expectation forecast of the BL(P,0,1,1) model.On the side, we estimate parameters in the USBL(1,0,1) model with the method of moment estimation, the method is shown by the simulation.At last,some advice is offered on the bilinear time series model studying.