Robust Two-Sample Mean Inference under Serial Dependence

TL;DR

This paper introduces robust two-sample mean tests for time series data that handle heterogeneity and dependence, utilizing novel t-tests and bootstrap methods for improved finite-sample performance.

Contribution

It develops a new framework for two-sample mean inference in time series, including HAR t-tests with adjusted degrees of freedom and a series-based wild bootstrap method.

Findings

Valid inference under heterogeneity and dependence

Enhanced finite-sample performance of bootstrap tests

Applicability to structural breaks and panel data

Abstract

We propose robust two-sample tests for comparing means in time series. The framework accommodates a wide range of applications, including structural breaks, treatment-control comparisons, and group-averaged panel data. We first consider series HAR two-sample t-tests, where standardization employs orthonormal basis projections, ensuring valid inference under heterogeneity and nonparametric dependence structures. We propose a Welch-type t-approximation with adjusted degrees of freedom to account for long-run variance heterogeneity across the series. We further develop a series-based HAR wild bootstrap test, extending traditional wild bootstrap methods to the time-series setting. Our bootstrap avoids resampling blocks of observations and delivers superior finite-sample performance.