In this chapter, we review nonlinear models for vector time series data and develop new nonparametric estimation and inference for them. Vector time series data exist widely in practice. In financial markets, multiple time series are usually correlated. When analyzing several interdependent time series, in general one should consider them as a single vector time series fitted by multivariate models, which provides a useful tool for modeling interdependencies among multiple time series and for simultaneously analyzing feedback and Granger causality effects. Since nonlinear features are widely observed in time series, we consider nonlinear methodology for modeling nonlinear vector time series data, which allows flexibility in the model structure and avoids the curse of dimensionality.

Pneumatic operated spring-diaphragm actuator is the most popular acting device in industrial applications. Precise modelling of pneumatic actuator continues to remain a major challenge because of its nonlinear characteristic. In this work, the characteristics of pneumatic actuator are analysed in details, and then the dynamic model, which considers effects of stem friction and compressibility of air, is developed. Computer simulation and experimental tests have been carried out on the developed model. The results show the model has a better performance.