Residual processes of nonlinear time series models and unit root tests

非线性时间序列模型的残差过程和单位根检验

• 批准号: 170202-2007
• 负责人: Yu, Hao
• 金额: $ 1.53万
• 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: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=364787
• 关键词: Residual; processes; nonlinear; time; series

The first part of proposed research is to construct and study residual processes based on nonlinear time series models such as GARCH and related models. The second part is to study unit root tests based on exact maximum likelihood estimation (MLE). The objectives of this research are threefold.1. Construct and study residual processes based on nonlinear time series models. A residual process is a stochastic process constructed from residuals of a specific model. One such process is the high moment partial sum process (HMPSP). New results for other nonlinear time series such as GARCH-in-mean and cointegrated regressions models will be attempted. Another residual process that will be studied is a modified empirical distribution process. The new approach is to construct empirical distribution processes based modified residuals. Several publications on this subject are expected.2. Study unit root tests based on exact MLE. The exact MLE has a unique feature that it is always less than 1 and is mainly used in stationary AR(1) time series. Further study is needed in order to find its limiting distribution under integrated AR(1) models with GARCH or other dependence structure errors. Limit distribution of the exact MLE for nearly integrated AR(1) models will be studied as well. Empirical and theoretical studies of the unit root tests are expected to generate several publications.3. Use R package Rmpi designed by applicant to implement parallel computation based Mackinnon's response surface regression technique. In order to conduct statistical inferences, mass simulation must be computed for different sample sizes and quantiles. A general procedure will be implemented in Rmpi so that users can find out P values and quantiles quickly with highly accurate results. This will lead to one or two publications.

拟议研究的第一部分是基于非线性时间序列模型（例如GARCH和相关模型）构建和研究剩余过程。第二部分是根据精确的最大似然估计（MLE）研究单位根测试。这项研究的目标是三倍。1。基于非线性时间序列模型构建和研究剩余过程。残差过程是由特定模型的残差构成的随机过程。这样的过程之一是高力矩部分总和过程（HMPSP）。将尝试针对其他非线性时间序列（例如均值和协整回归模型）的新结果。将研究的另一个剩余过程是修改的经验分布过程。新方法是构建基于经验分布过程的基于经验的修改残差。预计该主题的几个出版物2。研究单位根测试基于精确的MLE。确切的MLE具有独特的功能，它始终小于1，并且主要用于固定AR（1）时间序列。为了在集成的AR（1）模型中找到其限制分布，具有GARCH或其他依赖性结构误差。还将研究几乎集成AR（1）模型的精确MLE的限制分布。单位根检验的经验和理论研究有望产生多个出版物3。使用申请人设计的R软件包RMPI来实现基于Mackinnon的响应表面回归技术。为了进行统计推断，必须针对不同的样本量和分位数计算质量模拟。一般过程将在RMPI中实施，以便用户可以快速找到P值和分位数，并具有高度准确的结果。这将导致一两个出版物。