Statistical Inference for Long Memory and Nonlinear Time Series

该建议旨在开发用于长记忆和/或非线性时间序列的统计推断的方法和理论工具，而为线性ARMA类型序列开发的传统方法和理论对此并不适用。随着长记忆和非线性模型应用的迅速发展，迫切需要为现有方法提供理论依据，或者提出能够适应长记忆和非线性特征的新方法。为了满足这一需要，研究者建议研究以下问题：谱均值和比率统计量的可信区间；具有不相关但相依误差的分数次积分时间序列的白估计和诊断检验；两个平稳时间序列之间独立性和非相关性的新检验；二元分数次积分非线性时间序列的频域半参数推断。它们都与具有非线性特征的长/短时间序列的二阶性质相联系，共同涵盖了这类序列的一系列重要推断问题。具有长记忆和非线性的时间序列广泛存在于大气科学、环境科学、地球物理、水文、经济、金融等各个领域。这项工作将极大地加强现有的方法和理论，提供更多的工具，并在所有这些领域都有潜在的应用。拟议的研究通过让博士生直接参与拟议的研究并将结果纳入研究生统计课程，对教育产生重大影响。

The proposal aims to develop methodological and theoretical tools for statistical inference of long memory and/or nonlinear time series, for which the traditional methods and theory developed for linear ARMA-type series are not known to be applicable. Since the applications of long memory and nonlinear models are rapidly growing, there is an urgent and crucial need to either provide a theoretical justification for existing methods or propose novel methods that are able to accommodate long memory and nonlinear features. To meet this need, the investigator proposes to study the following research problems: confidence interval for spectral means and ratio statistics; Whittle estimation and diagnostic checking for fractionally integrated time series with uncorrelated but dependent errors; new tests of independence and non-correlations between two stationary time series; frequency domain semiparametric inference for bivariate fractionally integrated nonlinear time series. All of them are linked to the second order properties of the long/short time series with nonlinear features, and together, they cover a wide spectrum of important inference issues for such series.Time series with long memory and nonlinearities occur in various fields, including atmosphere science, environmental science, geophysics, hydrology, economics, finance and others. This work will greatly enhance the available methodologies and theories, provide more tools and have potential applications in all such fields. The proposed research has significant impact on education through involvement of Ph.D students directly in the proposed research and incorporation of results into graduate statistical courses.