A logic for causal inference in time series with discrete and continuous variables
Samantha Kleinberg
Many applications of causal inference, such as finding the relationship between stock prices and news reports, involve both discrete and continuous variables observed over time. Inference with these complex sets of temporal data, though, has remained difficult and required a number of simplifications. We show that recent approaches for inferring temporal relationships (represented as logical formulas) can be adapted for inference with continuous valued effects. Building on advances in logic, we introduce PCTLc (an extension of PCTL with numerical constraints) to allow representation and inference of relationships with a mixture of discrete and continuous components. We show that finding significant relationships in the continuous case can be done using the conditional expectation of an effect, rather than its conditional probability. We evaluate this approach on both synthetically generated and actual financial market data, showing that it can allow us to answer different questions than the discrete approach can.