Research On Modeling Of Multivariate Nonlinear Nonstationary Time Series

Nonstationarity and nonlinearity are the main properties of many economic and financial time series, and the test and estimation of nonlinear relation of multivariate nonstationary time series are important research areas in econometrics. Nonlinear regression and nonlinear cointegration of multivariate nonstationary time series are discussed in this dissertation, and the persistence and copersistence in conditional higher moments are considered in a uniform frame. The main work and innovations of the dissertation include:(1) The condition for the linear combination of VARFIMA process having ARMA expression is given, the relation of the existence of cointegration and the integration order of independent components is discussed by using independent components analysis(ICA) method, and the structure of cointegrating vector space is given.(2) The threshold t-GARCH model with structural change is proposed by associating the method of structural change with t-GARCH model, and the spurious persistence and spurious copersistenc of multivariate t-GARCH model with structural change are considered.(3) Persistence and copersistence in conditional moments of time series is proposed based on the concept of nonlinear integration, the equivalence of cointegration and copersistence in variance is proved, the uniform express is constructed to study cointegration and copersistence as an integration, and persistence and copersistence in conditional skewness and kurtosis are considered as the extended cases. Then the sufficient and necessary condition for persistence and copersistence in conditional moments of ARMA-GARCHSK model is studied, and the error correction expression of this model is given.(4) The asymptotic distribution of regular transformation of normalized fractionally integrated process and the integrable transformation and asymptotically homogeneous transformation of original process are developed, and based on these results the parametric estimator of nonlinear regression of fractionally integrated process is considered.(5) The asymptotic theory for the NW estimator and local polynomial estimator are developed when two independent integrated processes are used in a nonlinear regression. (6) Local polynomial estimator of nonlinear cointegration and nonlinear copersistence is studied, and two empirical research are given based on this method.(7) Kernel density estimation of fractionally integrated process is considered, and the asymptotic distribution of parametric and nonparametric estimators of nonlinear regression of fractionally integrated processes are given.The research is supported by National Natural Science Foundation of China: Research on Long Run Equilibrium in Multivariate Moments Series and Avoiding Tactics of Dynamic Financial Risk (No: 70471050).