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

这个项目考虑了关于长记忆时间序列的最新主题的几个问题，包括分数协整、数据缩减和错误指定的长记忆模型的估计。第一个研究方向是开发和实现分数协整多变量时间序列的新统计方法。重点是将协整向量空间分成产生不同记忆参数的子空间。第二个主要研究主题是数据渐变及其应用。介绍了一种数据锥化生成算法。该算法可以很容易地生成任意阶数的数据锥化。这类新的锥形具有更好的方差性质，并且得到的周期图是平移不变的，这是估计长记忆过程参数的理想性质。第三条研究路线解决了估计错误指定的长记忆模型及其含义的问题。对错误指定的长记忆模型的频域极大似然估计的研究表明，即使时间序列的长记忆结构被正确指定，对短记忆动态的错误指定也可能导致参数估计小于根n相容和非高斯。这些非标准的渐近结果导致了长记忆过程的渐近有效的模型选择和有效的矩估计方法(EMM)的研究，因为这两个过程都假设错误指定的模型已经被估计。该项目是德克萨斯农工大学社会科学和统计学领域正在进行的一项新计划的一部分。这一倡议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动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.