Fractional Cointegration, Tapering and Estimation of Misspecified Models in Long Memory Time Series

该项目考虑了长记忆时间序列中最新主题的几个问题，包括分数协整，数据逐渐变细和错误指定长记忆模型的估计。研究的第一线开发和实现了分数协整多元时间序列的新统计方法。重点是将协整向量空间划分为产生不同内存参数的子空间。第二个主要研究课题是数据锥及其应用。介绍了一种数据锥度生成算法。该算法可以方便地生成任意顺序的数据锥。这类新圆锥具有较好的方差特性，并且得到的周期图具有平移不变性，这是估计长记忆过程参数的理想特性。研究的第三条线解决了估计错误指定的长记忆模型及其影响的问题。对长记忆模型的频域最大似然估计的研究表明，即使正确指定了时间序列的长记忆结构，短记忆动力学的错误指定也可能导致参数估计小于n根一致和非高斯。这些非标准渐近结果导致了对长记忆过程的渐近有效模型选择和有效矩量法（EMM）估计的研究，因为这两种方法都假设已经估计了一个错误的模型。这个项目是德克萨斯农工大学社会科学与统计学新项目正在进行的一部分。该计划的一个主要组成部分涉及心理学、经济学、政治学和统计学之间的相互作用，以研究时间序列技术在推进科学和决策方面发挥关键作用的问题。

This project considers several problems on the most recent topics in long memory time series including fractional cointegration, data tapering and estimation of misspecified long memory models. The first line of research develops and implements new statistical methods for fractionally cointegrated multivariate time series. The focus is on separating the space of cointegrating vectors into subspaces yielding different memory parameters. The second main research topic focuses on data tapers and their applications. A data taper generating algorithm is introduced. The proposed algorithm can easily generate data tapers of any order. This class of new tapers has better variance properties and the resulting periodogram is shift-invariant, a desirable property in estimating parameters of long memory processes. The third line of research addresses the problems of estimating misspecified long memory models and their implications. A study of the frequency domain maximum likelihood estimators of misspecified long memory models suggests that even if the long memory structure of the time series is correctly specified, misspecification of the short memory dynamics may result in parameter estimators which are less than root-n-consistent and non-Gaussian. These nonstandard asymptotic results lead to a study of asymptotically efficient model selection and Efficient Method of Moments (EMM) estimation for long memory processes, because both procedures assume that a misspecified model has been estimated. This project is part of ongoing development of a new initiative in Social Science and Statistics at Texas A&M University. A major component of this initiative involves interaction between psychology, economics, political science and statistics to study issues where techniques in time series play the key role in advancing science and decision making.