5. Conclusions

Figure 1. The power curves for Example 1. Significance level is 5%.

102 Time Series Analysis and Applications

In this chapter, we have reviewed some parametric and nonparametric methods for modeling nonlinear vector time series data, which include the VAR model, the multivariate threshold autoregressive model, and the multivariate functional-coefficient regression model. These models have great significance in econometrical and statistical theory and application. Based on the weighted local least square estimation, we have proposed a variable selection method for the functional-coefficient model. This model selection procedure is applicable to the proposed multivariate single index models and multivariate time-varying coefficient models. We have also extended the generalized likelihood ratio test to the time-varying coefficient model and demonstrated its performance through simulation. The proposed methodology is very useful for modeling nonlinear dynamic structures inherited in financial data. However, there are many problems remain unsolved for our procedure, such as the limiting theory about the proposed methodology. Future work includes, but not limited to, extending our models to nonstationary settings and exploring their performance in different applications.
