A bias reduced long run variance estimator with a new first-order kernel

Abstract

This paper presents a theoretical analysis of a bias-reduced long run variance (LRV) estimator in a simple location model with unknown mean. This LRV estimator uses a new kernel expressed as a weighted sum of two characteristic exponent $q=1$ kernels to approximate the estimator proposed by Yang and Vogelsang (2018). This new kernel effectively reduces biases from autocovariance estimation and kernel downweighting, addressing the Parzen bias missed by fixed-bandwidth asymptotics. When applied to testing the mean in a simple location model, the bias reduced approach improves the size-power tradeoff in $t$-tests in finite samples, reducing over-rejections faster than power loss as the bandwidth increases. The new kernel requires a smaller bandwidth than the Bartlett kernel under serial correlated errors to achieve the same null rejection probability. Smaller bandwidths also ensure positive semi-definiteness of this bias reduced LRV estimator for the bandwidths that optimize the testing’s size and power tradeoff in finite samples. A comparison with the Bartlett, quadratic spectral, and EWC estimators demonstrates the benefits of the proposed nearly unbiased method in hypothesis testing.