AUTOMATIC POSITIVE SEMIDEFINITE HAC COVARIANCE MATRIX AND GMM ESTIMATION
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.
c1 Address correspondence to Richard J. Smith, Department of Economics, University of Warwick, Coventry CV4 7AL, U.K.; e-mail: email@example.com.