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，这些方法和理论是为线性arma型序列开发的传统方法和理论所不适用的。由于长记忆和非线性模型的应用正在迅速增长，因此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。为了满足这一需求，研究者提出了以下研究问题：谱均值的置信区间和比值统计；误差不相关但相关的分数积分时间序列的Whittle估计与诊断检验平稳时间序列独立性和非相关性的新检验二元分数积分非线性时间序列的频域半参数推理。它们都与具有非线性特征的长/短时间序列的二阶性质有关，它们共同涵盖了这类序列的广泛的重要推理问题。具有长记忆和非线性的时间序列存在于大气科学、环境科学、地球物理、水文、经济、金融等各个领域。这项工作将大大加强现有的方法和理论，提供更多的工具，并在所有这些领域具有潜在的应用。建议的研究通过博士生直接参与建议的研究并将结果纳入研究生统计课程，对教育产生了重大影响。

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.