ZHOU Yongzheng

(Basic Course Department)

Abstract: This article gives a comprehensive description of several discrete nonlinear time series models and volterra nonlinear systems, and summarizes some of the issues currently being discussed.People use linear time series models to describe a lot of dynamic data, and have obtained good results in many fields. The work of BOX and Jenkins (1970) undoubtedly played an important role. During1970 to 1980, linearity and Gaussian properties became increasingly clear. Although they are useful concepts in many respects, they are still unclear, and unrealistic assumptions are beyond the first approximation of many practical situations. More in-depth research has found many phenomena and problems. It is not enough to describe them with linear models, and the effect is also poor. This motivates people to further study nonlinear time series models.So far, many mathematical statistics workers at home and abroad have studied a large number of practical problems and put forward some nonlinear time series models. This article is a review article written with reference to many domestic and foreign documents.

Keywords: volterra, nonlinear time series