We propose a parametric spectral estimation procedure for contructing heteroskedasticity and autocorrelation consistent (HAC) covariance matrices. We establish the consistency of this procedure under very general conditions similar to those considered in previous research. We also perform Monte Carlo simulations to evaluate the performance of this procedure in drawing reliable inferences from linear regression estimates. These simulations indicate that the parametric estimator matches, and in some cases greatly exceeds, the performance of the prewhitened kernel estimator proposed by Andrews and Monahan (1992). These simulations also illustrate the inherent limitations of non-parametric HAC covariance matrix estimation procedures, and highlight the advantages of explicitly modeling the temporal properties of the error terms.