Inference Optimal Long Run Variance Estimation with Lugsail Kernels

2026-06-15

AI Summary

This study addresses the significant negative bias of existing spectral variance estimators under positively correlated data and the absence of an optimal bandwidth selection rule for lugsail kernels. Focusing on stationary data with unknown serial correlation, the work establishes, for the first time, an inference-optimal bandwidth rule for the lugsail long-run variance estimator based on a nonstandard fixed-smoothing asymptotic distribution. This rule achieves zero asymptotic bias under arbitrary dependence structures while balancing bias correction and estimation variability. Theoretical analysis and simulation experiments demonstrate that the proposed method substantially reduces estimation bias and enhances the robustness and accuracy of statistical inference.

Abstract

For datasets with unknown but stationary serial dependence, a robust long run variance estimator is essential to handle diverse scenarios. Spectral variance estimators are commonly used but tend to exhibit significant negative bias in the presence of positive correlation. To overcome this, zero lugsail estimators have been introduced, offering zero asymptotic bias regardless of the correlation structure. However, there are currently no guidelines for selecting the optimal bandwidth for lugsail estimators, a critical component in the estimation process. We propose an inference optimal bandwidth rule for lugsail estimators, based on nonstandard fixed-smoothing limiting distributions developed in our study. This approach significantly improves bias correction, accounts for variability, and provides an estimator optimized for robust inference. Our theoretical findings are supported by a simulation study.

Problem

• long run variance
• lugsail kernels
• bandwidth selection
• serial dependence
• robust inference

Innovation

• lugsail kernel
• long run variance
• inference optimal bandwidth
• fixed-smoothing asymptotics
• spectral variance estimator