Research On Nonlinear Time Series Model And Empirical Analysis

People in the financial markets tend to focus on the return of financial products, and there exist always some nonlinear features such as volatility clustering phenomenon in return series. The nonlinear time series models, including parametric models such as ARCH model, TAR model, and nonparametric models such as AAR model, NAR model, have obvious advantages to model the nonlinar features such as asymmetry, long memory, heteroscedasticity, nonlinear auto-dependency and other aspects. Therefore, it is able to provide a broader perspective for finance academics and financial investors to apply nonlinear time series analysis to research financial data.Some nonlinear time series models commonly used are briefly describedin this paper firstly; the causes of "curse of dimensionality" in nonparametric methods is prsented; the tests of nonlinear features based on graphical way and generalized liklihood ratio statistics are expressed respectively; the identification of auto-dependency based on GLR test is discussed; the reasons why composite nonlinear models are needed are explained and some of the estimations of composite models (including NAR-ARMA model, NAR-parameters AR-GARCH models) are suggested.The CBOT soybean futures data is studied in this paper by applying nonlinear time series analysis, and of which, the internal dynamic laws and relationship with some other factors are researched, and the results are as follows:There is siginificant nonlinear auto-dependency in CBOT soybean futures return series;U.S. soybean growth vigour affects significantly the corresponding futures return in a nonlinear way;There are some other factors affecting return in a nonlinear way.At last, for soybean return data, a parametric composite nonlinear model and nonparametric composite nonlinear model are fitted, viz. AR-GARCH model and NAR-AR-ARCH model respectively. Furthermore, the goodness of fit shows that NAR-AR-GARCH model is more suitable for sample data, which is in accordance with nonlinear auto-dependency of return series, and also it shows that nonlinear composite model is suitable and effective for analyzing financial time series.