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

A new family of kernels is suggested for use in heteroskedasticity and autocorrelation consistent (HAC) and long run variance (LRV) estimation and robust regression testing. The kernels are constructed by taking powers of the Bartlett kernel and are intended to be used with no truncation (or bandwidth) parameter. The news kernels, called sharp origin kernels, can be used in regression testing in much the same way as conventional kernels with no truncation, as suggested in the work of Kiefer and Vogelsang. 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. If rho is passed to infinity with the sample size (T), the new kernels provide consistent HAC and LRV estimates as well as continued robust regression testing. Simulations show that in regression testing with the sharp origin kernel, the power properties are better than those with simple untruncated kernels (where rho =1) and at least as good as those with truncated kernels. Size is generally more accurate with sharp origin kernels than truncated kernels. In practice a simple fixed choice of the exponent parameter around rho=16 for the sharp origin kernel produces favorable results for both size and power in regression testing with sample sizes that are typical in econometric applications.