Robust Two-Sample Inference under Serial Dependence

2025/12/12 by Ulrich Hounyo, Min Seong Kim, Hounyo, Ulrich +1
Mathematics · #Advanced Causal Inference Techniques #Statistical Methods and Inference #Statistical Methods and Bayesian Inference

paper · pdf · doi:10.48550/arxiv.2512.11259

Abstract

We propose robust inference for two-sample comparison with time-series data under serial dependence and heterogeneous long-run variances. Standardizing with orthonormal-basis (series HAR) projections, we develop two-sample t-tests and, for joint hypotheses on a vector of means, a series HAR Wald statistic. Because the increasing-K chi-square limit tends to over-reject, we propose Welch-type fixed-K t- and F-approximations with adjusted degrees of freedom. We further develop a series HAR wild bootstrap that reproduces serial dependence without resampling blocks. The framework nests difference-in-differences and Diebold-Mariano testing. Simulations and two empirical applications show accurate size control and competitive power, a tuning-free alternative to cluster-based inference.

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