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

本计画主要探讨长记忆时间序列的几个最新议题，包括分数阶共整合、资料渐减与错误指定长记忆模型的估计。研究的第一线开发和实施分数协整多元时间序列的新的统计方法。重点是分离的空间cointegrating向量到子空间产生不同的内存参数。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。所提出的算法可以很容易地产生任何阶的数据锥。这类新的锥度有更好的方差特性和由此产生的周期图是移位不变的，在估计长记忆过程的参数的一个理想的属性。第三条研究路线解决了估计错误指定的长记忆模型及其影响的问题。错误指定的长记忆模型的频域最大似然估计的研究表明，即使正确指定的时间序列的长记忆结构，错误指定的短记忆动态可能会导致参数估计是小于根-n-一致的和非高斯。这些非标准的渐近结果导致渐近有效的模型选择和有效的矩量法（EMM）估计的长记忆过程的研究，因为这两个程序假设一个错误指定的模型已估计。该项目是在得克萨斯州农工大学社会科学和统计学的一个新的倡议正在进行的发展的一部分。这一举措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，以研究时间序列中的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.