Validating causal inference in time series models with conditional-independence tests

Ecologists often use time-series models to approximate dynamics arising from density dependence, species interactions, community synchrony, and other processes. Dynamic structural equation models can represent simultaneous and lagged interactions among variables with missing data, and therefore encompasses a wide family of analyses (linear regression, vector autoregressive models, and dynamic factor analysis). However, their interpretation as structural causal models (i.e., counterfactual analysis) requires validating that the assumed dynamics are consistent with available data. In site-replicated and phylogenetic contexts, ecologists validate causal assumptions by testing implied conditional-independence relationships (a directional-separation or “d-sep” test), but this has not been extended to include simultaneous and lagged effects in time-series contexts. Here, we propose a time-series d-sep test and use a simulation experiment and case studies to explore its performance. The simulation confirms that this test results in a uniform p-value when using a correct causal model, and a low p-value (i.e., a decision to reject a model) when the causal model is incorrect. As expected, time-series that are short or have a large proportion of missing data then have less power to reject an incorrect model. In a novel application involving pollock in the Gulf of Alaska, the test supports a conceptual model where temperature drives spawning phenology, which subsequently affects survey availability for a spawning survey. In a previously published analysis involving wolf-moose interactions in Isla Royale, the test supports top-down control but cannot distinguish whether bottom-up control is supported. We conclude that d-sep is a useful test to evaluate the structural validity of a time-series model, allowing ecologists to make better causal inference about dynamical systems from correlated time series data.