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

Texas A&M Research Foundation, College Station TX

Investigators

Abstract

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.