多元非线性非平稳时间序列的建模方法研究
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摘要
非平稳性和非线性性是多数经济和金融时间序列的主要特性,如何检验和估计多元非平稳时间序列之间的非线性关系一直是一个非常重要的研究课题。本文重点讨论多元非平稳时间序列的非线性回归和非线性协整问题,并在条件矩的统一框架下考虑了线性协整和线性协同持续的关系并进一步考虑了条件高阶矩的持续性和协同持续性。论文的主要工作和创新如下:
(1)给出了向量ARFIMA过程的线性组合具有ARMA过程表示形式的充分必要条件,其次基于独立成分分析的方法讨论了向量ARFIMA过程存在分数维协整关系与其独立成分的关系,讨论了分数维协整向量空间的结构。
(2)结合t-GARCH模型和变结构的方法提出了变结构t-GARCH模型,并考虑了多元变结构GARCH模型产生的伪持续和伪协同持续性问题。
(3)从预测的角度给出了时间序列矩持续的定义,证明了由Granger所提出的协整概念以及由Bollerslev和Engle所给出的波动协同持续概念分别是矩持续的两种特殊情形,从而从矩持续理论构建了单整和波动持续的统一框架,并提出了三阶矩和四阶矩持续和协同持续的概念;然后在ARMA-GARCHSK模型体系下讨论了时间序列矩持续的充分必要条件;最后给出了向量ARMA-GARCHSK模型矩协同持续存在的充分必要条件及其误差修正模型。
(4)给出了标准化分整过程正则变换的渐近性质,进一步讨论了分整过程的可积变换和渐近齐次变换的渐近性质,并利用上述结果讨论了分整过程非线性回归中参数估计的渐近分布。
(5)考虑了两个独立单整过程的非参数伪回归问题,得到了非线性关系的NW核估计和局部多项式估计的渐近分布。
(6)考虑了非线性协整和非线性协同持续关系的局部多项式估计方法,并用该方法给出了两个实证研究。
(7)考虑了分整序列的核密度估计,给出了分整序列非线性回归参数方法的渐近性质,最后讨论了分整序列非线性回归的NW核估计和局部多项式估计的渐近性质。
本论文是国家自然科学基金资助项目《多变量矩序列长期均衡关系及动态金融风险规避策略研究》(No: 70471050)的组成部分。
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).
(1)给出了向量ARFIMA过程的线性组合具有ARMA过程表示形式的充分必要条件,其次基于独立成分分析的方法讨论了向量ARFIMA过程存在分数维协整关系与其独立成分的关系,讨论了分数维协整向量空间的结构。
(2)结合t-GARCH模型和变结构的方法提出了变结构t-GARCH模型,并考虑了多元变结构GARCH模型产生的伪持续和伪协同持续性问题。
(3)从预测的角度给出了时间序列矩持续的定义,证明了由Granger所提出的协整概念以及由Bollerslev和Engle所给出的波动协同持续概念分别是矩持续的两种特殊情形,从而从矩持续理论构建了单整和波动持续的统一框架,并提出了三阶矩和四阶矩持续和协同持续的概念;然后在ARMA-GARCHSK模型体系下讨论了时间序列矩持续的充分必要条件;最后给出了向量ARMA-GARCHSK模型矩协同持续存在的充分必要条件及其误差修正模型。
(4)给出了标准化分整过程正则变换的渐近性质,进一步讨论了分整过程的可积变换和渐近齐次变换的渐近性质,并利用上述结果讨论了分整过程非线性回归中参数估计的渐近分布。
(5)考虑了两个独立单整过程的非参数伪回归问题,得到了非线性关系的NW核估计和局部多项式估计的渐近分布。
(6)考虑了非线性协整和非线性协同持续关系的局部多项式估计方法,并用该方法给出了两个实证研究。
(7)考虑了分整序列的核密度估计,给出了分整序列非线性回归参数方法的渐近性质,最后讨论了分整序列非线性回归的NW核估计和局部多项式估计的渐近性质。
本论文是国家自然科学基金资助项目《多变量矩序列长期均衡关系及动态金融风险规避策略研究》(No: 70471050)的组成部分。
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).
引文
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