Thesis:the Order Determination Of The Bilinear Time Series Model By Lasso Methods

In recent years, there are many discussions and methods about the BL(p,q,P,Q) model, such as the genetic algorithm. However, there is a common shortcoming in these methods, that they do not produce sparse models. In order to solve this problem, we will focus on the applications of the Lasso method about the BL model. Comparing with traditional regression methods, it has the advantage of reducing the coefficients of the model.In this article,the BL model will be fitted by the GLLS method,which is the combination of the Lasso method, the generalized cross-validation method(GCV), the least angle regression method (Lars) and the stepwise regression method (Step).In addition,by the analysis of the data simulation and the instance of the application, we show that not only the model is simple and accuracy, but also converges to the global optimal solution, which leads to the greater stability of the model.