Time Series Experiments and Causal Estimands: Exact Randomization Tests and Trading

Abstract

We define causal estimands for experiments on single time series, extending the potential outcome framework to dealing with temporal data. Our approach allows the estimation of a broad class of these estimands and exact randomization-based p-values for testing causal effects, without imposing stringent assumptions. We further derive a general central limit theorem that can be used to conduct conservative tests and build confidence intervals for causal effects. Finally, we provide three methods for generalizing our approach to multiple units that are receiving the same class of treatment, over time. We test our methodology on simulated “potential autoregressions,” which have a causal interpretation. Our methodology is partially inspired by data from a large number of experiments carried out by a financial company who compared the impact of two different ways of trading equity futures contracts. We use our methodology to make causal statements about their trading methods. Supplementary materials for this article are available online.

Keywords:

• Causality
• Nonparametric
• Potential outcomes
• Trading costs

Acknowledgments

We thank Edo Airoldi, Joshua Angrist, Guillaume Basse, Stephen Blyth, Peng Ding, Pierre Jacob, Guido Kuersteiner, Anthony Ledford, Daniel Lewis, Fabrizia Mealli, Xiao-Li Meng, Luke Miratrix, Susan Murphy, David Parkes, Mikkel Plagborg-Moller, James M. Robins, Donald B. Rubin, Jim Stock, and Panos Toulis for various suggestions, and AHL Partners LLP (London, UK) for giving us the financial data we use.