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.