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

Jingjing Yang and Timothy J. Vogelsang

Economics Letters, 2025, vol. 252, issue C

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.

Keywords: Long run variance; HAR estimator; Bias correction; Fixed-b asymptotics; Hypothesis testing; Size power tradeoff (search for similar items in EconPapers)
JEL-codes: C12 C13 C14 C22 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecolet:v:252:y:2025:i:c:s0165176525001776

DOI: 10.1016/j.econlet.2025.112340

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