A Fast Algorithm for the Computation of HAC Covariance Matrix Estimators

Abstract

This paper considers the algorithmic implementation of the heteroskedasticity and autocorrelation consistent (HAC) estimation problem for covariance matrices of parameter estimators. We introduce a new algorithm, mainly based on the fast Fourier transform, and show via computer simulation that our algorithm is up to 20 times faster than well-established alternative algorithms. The cumulative effect is substantial if the HAC estimation problem has to be solved repeatedly. Moreover, the bandwidth parameter has no impact on this performance. We provide a general description of the new algorithm as well as code for a reference implementation in R.

Keywords

• GMM
• HAC estimation
• Newey-West estimator
• Toeplitz matrices
• discrete Fourier transformation (DFT)
• R