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AUTOMATIC POSITIVE SEMIDEFINITE HAC COVARIANCE MATRIX AND GMM ESTIMATION

Published online by Cambridge University Press:  08 February 2005

Richard J. Smith
Richard J. Smith
Affiliation:
cemmap, U.C.L. and I.F.S. and University of Warwick
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Abstract

This paper proposes a new class of heteroskedastic and autocorrelation consistent (HAC) covariance matrix estimators. The standard HAC estimation method reweights estimators of the autocovariances. Here we initially smooth the data observations themselves using kernel function–based weights. The resultant HAC covariance matrix estimator is the normalized outer product of the smoothed random vectors and is therefore automatically positive semidefinite. A corresponding efficient GMM criterion may also be defined as a quadratic form in the smoothed moment indicators whose normalized minimand provides a test statistic for the overidentifying moment conditions.

Type
Research Article
Information
Econometric Theory , Volume 21 , Issue 1 , February 2005 , pp. 158 - 170
Copyright
© 2005 Cambridge University Press

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