12 A practitioner's guide to robust covariance matrix estimation

Abstract

This chapter discusses the concept of robust covariance matrix estimation. In many structural economic or time-series models, the errors may have heteroscedasticity and temporal dependence of unknown form. Thus, to draw accurate inferences from estimated parameters, it has become increasingly common to construct test statistics using a heteroskedasticity and autocorrelation consistent (HAC) or robust covariance matrix. The key step in constructing a HAC covariance matrix is to estimate the spectral density matrix at frequency zero of a vector of residual terms. In some empirical problems, the regression residuals are assumed to be generated by a specific parametric model. In a rational expectations model, for example, the Euler equation residuals typically follow a specific moving-average (MA) process of known finite order. HAC covariance matrix estimation procedures can be classified into two broad categories: nonparametric kernel-based procedures and parametric procedures. Each kernel-based procedure uses a weighted sum of the auto-covariances to estimate the spectral density at frequency zero, where the weights are determined by the kernel and the bandwidth parameter. Each parametric procedure estimates a time-series model and then constructs the spectral density at frequency zero that is implied by this model.