Consistency of kernel variance estimators for sums of semiparametric linear processes

Abstract

Conditions are derived for the consistency of kernel estimators of the variance of a sum of dependent heterogeneous random variables, with a representation as moving averages of near-epoch dependent functions of a mixing process. Fourth moments are not generally required. The conditions permit more dependence than a purely non-parametric representation allows, and may be close to those of the best-known conditions for the functional central limit theorem. The class of permitted kernel functions is different from those usually considered, but can approximate most of the usual choices arbitrarily closely, and can be extended to include them subject to a seemingly innocuous extra condition on the random process. ABSTRACT FROM AUTHOR Copyright of Econometrics Journal is the property of Blackwell Publishing Limited and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts) Conditions are derived for the consistency of kernel estimators of the variance of a sum of dependent heterogeneous random variables, with a representation as moving averages of near-epoch dependent functions of a mixing process. Fourth moments are not generally required. The conditions permit more dependence than a purely non-parametric representation allows, and may be close to those of the best-known conditions for the functional central limit theorem. The class of permitted kernel functions is different from those usually considered, but can approximate most of the usual choices arbitrarily closely, and can be extended to include them subject to a seemingly innocuous extra condition on the random process. ABSTRACT FROM AUTHOR Copyright of Econometrics Journal is the property of Blackwell Publishing Limited and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts)