Consistent HAC Estimation and Robust Regression Testing Using Sharp Origin Kernels with No Truncation

Sharp origin kernels, constructed by taking powers of the Bartlett kernel, are suggested for use in heteroskedasticity and autocorrelation consistent (HAC) estimation with no truncation (or bandwidth) parameter. When the power parameter (rho) is fixed, analysis and simulations indicate that sharp origin kernels lead to tests with improved size properties relative to conventional tests and better power properties than other tests using Bartlett and other conventional kernels without truncation. When the power parameter is passed to infinity with the sample size (T), the new kernels provide consistent HAC estimates. A data-driven method for selecting the power parameter is recommended for hypothesis testing. A new test procedure that combines the good elements of fixed rho and large rho asymptotics is suggested. Simulations show that the new test is less size-distorted than the conventional HAC t-test at the cost of a very small power loss.