Statistical Inference for Nonlinear Time Series and Parallel Statistical Computing

非线性时间序列的统计推断和并行统计计算

• 批准号: 170202-2012
• 负责人: Yu, Hao
• 金额: $ 0.87万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=569556
• 关键词: Statistical; Inference; Nonlinear; Time; Series

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.

拟议的研究主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领域的持续研究以及并行的统计计算及其的方面 申请。拟议的研究的第一部分是继续基于非线性时间序列模型（例如GARCH和相关模型）来处理剩余过程。第二部分是研究多元GARCH模型，发展相应的QMLE一致性和正态性的渐近理论，并提供自适应套索程序。第三部分是继续开发用于并行统计计算的RMPI软件包，并为多元GARCH模拟，空间统计模拟和长期死亡率预测构建新软件包。这项研究的目标是四倍。 1。基于非线性时间序列模型的构建和研究剩余过程。提出了修改的经验过程。将尝试针对其他非线性时间序列（例如均值和协调回归模型）的新结果。提出的经验过程的应用将是变更点问题，合适的测试和对称测试。 2。开发偶然模型的渐近理论，这是金融数学中经常使用的模型之一。 3。为多元GARCH模型开发渐近理论，并提供自适应套索程序 消除不需要的参数。应用程序是投资组合优化和风险评估，这是财务数学非常重要的领域。 4。继续开发RMPI软件包。 RMPI被认为是R社区中高性能和并行计算的两个核心软件包之一。它被广泛用于金融数学，生物信息学和蒙特卡洛模拟领域。