Statistical Inference for Nonlinear Time Series and Parallel Statistical Computing

**拟议的研究课题是我在线性和非线性时间序列的统计推断和模型诊断分析以及并行统计计算及其**应用领域继续研究的方面。研究的第一部分是继续研究基于非线性时间序列模型的残差过程，如GARCH模型和相关模型。第二部分研究了多元GARCH模型，发展了相应的QMLE相合性和正态的渐近理论，并给出了自适应LASSO过程。第三部分是继续开发用于并行统计计算的RMPI程序包，并建立用于多变量GARCH模拟、空间统计模拟和长期死亡率预测的新程序包。本研究的目的有四个方面。**1。基于非线性时间序列模型的残差过程的构建与研究。提出了一种改进的经验过程。还将尝试其他非线性时间序列的新结果，如GARCH均值和协整回归模型。所提出的经验过程的应用将是变点问题、拟合度检验和对称检验。**2.发展GARCH均值模型的渐近理论，这是金融数学中常用的模型之一。**3.发展多变量GARCH模型的渐近理论，并提供自适应套索程序**以消除不需要的参数。一个应用程序是投资组合优化和风险评估，这是金融数学的一个非常重要的领域。**4.继续开发RMPI包。RMPI被认为是R社区高性能和并行计算的两个核心包之一。它广泛应用于金融数学、生物信息学和蒙特卡罗模拟等领域。******************

**The proposed research topics are aspects of my continuing research in areas of statistical inference and model diagnostic analysis for linear and nonlinear time series as well as parallel statistical computing and its**applications. The first part of the proposed research is to continue to work on residual processes based on nonlinear time series models such as GARCH and related models. The second part is to study multivariate GARCH models, develop corresponding asymptotic theory of consistency and normality of QMLE, and provide adaptive LASSO procedure. The third part is to continue developing Rmpi package for parallel statistical computing and build new packages for multivariate GARCH simulation, spatial statistical simulation and long-term mortality prediction. The objectives of this research are fourfold.**1. Construct and study residual processes based on nonlinear time series models. A modified empirical process is proposed. New results for other nonlinear time series such as GARCH-in-mean and co-integrated regressions models will be attempted. Applications of the proposed empirical processes will be change-point problems, goodness-of-fit tests and symmetric tests.**2. Develop asymptotic theory for a GARCH-in-mean model, one of the often used models in financial mathematics.**3. Develop asymptotic theory for multivariate GARCH models as well as provide adaptive LASSO procedure**to eliminate un-needed parameters. An application is the portfolio optimization and risk assessment, a very important area of financial mathematics.**4. Continue developing Rmpi package. Rmpi is considered to be one of two core packages for High-Performance and Parallel Computing in R community. It is used widely in areas of financial mathematics, bioinformatics, and Monte Carlo simulation. ******************