Tight differencing in spectral density estimation with centrosymmetric kernels

2026-08-26

AI Summary

本文针对序列依赖数据中趋势波动或突变导致的传统方法失效问题，通过引入与紧差分兼容的中心对称核来改进谱密度估计。

Abstract

Mean-robust estimation of spectral density and long-run variance is crucial for many statistical inference procedures. However, existing methods often degrade when serially dependent data exhibit volatile, time-varying trends, or sudden jumps, particularly in small samples. While differencing and kernel averaging are standard tools for achieving mean robustness and consistency, they are not inherently compatible. Combining them can compromise optimality. Specifically, tight differencing, an operation of taking small-lag differences to enhance local de-trending, introduces strong correlations that distort the high-order properties of kernel-averaged estimators. To resolve this incompatibility, we introduce a novel class of centrosymmetric kernels explicitly designed to integrate with tight differencing. We demonstrate that the optimal tight difference sequence for serially dependent data differs from classical sequences designed for independent data. Notably, these proposed optimal sequences are data-independent and can be applied directly without pre-fitting. Finally, the proposed estimators are demonstrated to be useful across various statistical inference tasks, including tests for stationarity and white noise.

Problem

• spectral density
• long-run variance
• serially dependent data
• tight differencing
• kernel averaging

Innovation

• centrosymmetric kernels
• tight differencing
• serially dependent data
• mean-robust estimation