非线性时间序列的理论及其应用研究

The research purpose of the grant project is to study some important theoretic problems in nonlinear time series. For the general nonlinear time series models and some important parametric nonlinear time series models with application in many fileds, we gave some useful sufficient conditions of strict stationarity, ergodicity,.geometric ergodicity and the existence of high order moments of models. We proposed a new testing method for conditional heteroscedasticity of two kinds of parametric nonlinear time series models. We applied these results to statistical analysis of financial data.

非线性时间序列分析是现代统计学的主要研究课题之一。本项目重点研究这类模型的几何遍历性，时间序列的线性性和条件异方差的检验，非线性时间序列模型的定阶和部分线性时序模型的估计。利用本项目的理论研究成果，推动经济和金融等学科的研究，并为其提供理论基础。