2023/12/02 by Likai Chen, Chen, Likai, Georg Keilbar +5
Economics, Econometrics and Finance · Mathematics · #Advanced Causal Inference Techniques #Econometrics (econ.EM) #Energy, Environment, Economic Growth #FOS: Computer and information sciences #FOS: Economics and business #Methodology (stat.ME) #Spatial and Panel Data Analysis
paper · pdf · doi:10.48550/arxiv.2312.01162
openalex publication_date 2023/12/02 · openalex created_date 2023/12/06 · openalex updated_date 2026/07/28
We study simultaneous inference on jumps in the conditional mean functions of a high-dimensional collection of heterogeneous nonparametric time series, where the number of series may exceed the sample size and the data may exhibit strong cross-sectional dependence. The jump depends on one specific covariate, and we allow the regression function to vary with additional latent variables. We propose two uniform tests: one for the existence of jumps and one for their homogeneity across series. We derive a simple closed-form approximation to the covariance structure of the jump estimators and establish a high-dimensional Gaussian approximation showing that, owing to the localized construction of the statistics, the maximum of the studentized jumps is approximated by the maximum of independent Gaussians. The cross-sectional dependence is thus asymptotically negligible for critical values, even under strong (e.g., factor) dependence, and the approximation requires estimating only the variance for each series. For pronounced cross-sectional dependence, a dependence-aware refinement restores the off-diagonal covariances, improving finite-sample size and power. Simulations show accurate size and reasonable power under both cross-sectional and serial dependence, and two empirical applications reveal significant non-smooth effects.