Conditional independence testing with a single realization of a multivariate nonstationary nonlinear time series

Identifying relationships among stochastic processes is a key goal in disciplines that deal with complex temporal systems, such as economics. While the standard toolkit for multivariate time series analysis has many advantages, it can be difficult to capture nonlinear dynamics using linear vector autoregressive models. This difficulty has motivated the development of methods for variable selection, causal discovery, and graphical modeling for nonlinear time series, which routinely employ nonparametric tests for conditional independence. In this paper, we introduce the first framework for conditional independence testing that works with a single realization of a nonstationary nonlinear process. The key technical ingredients are time-varying nonlinear regression, time-varying covariance estimation, and a distribution-uniform strong Gaussian approximation.

Difference-in-Differences with Time-varying Continuous Treatments using Double/Debiased Machine Learning

We propose a difference-in-differences (DiD) method for a time-varying continuous treatment and multiple time periods. Our framework assesses the average treatment effect on the treated (ATET) when comparing two non-zero treatment doses. The identification is based on a conditional parallel trend assumption imposed on the mean potential outcome under the lower dose, given observed covariates and past treatment histories. We employ kernel-based ATET estimators for repeated cross-sections and panel data adopting the double/debiased machine learning framework to control for covariates and past treatment histories in a data-adaptive manner. We also demonstrate the asymptotic normality of our estimation approach under specific regularity conditions. In a simulation study, we find a compelling finite sample performance of undersmoothed versions of our estimators in setups with several thousand observations.