Causal discovery from temporally aggregated time series

Discovering causal structure of a dynamical system from observed time series is a traditional and important problem. In many practical applications, observed data are obtained by applying subsampling or temporally aggregation to the original causal processes, making it difficult to discover the underlying causal relations. Subsampling refers to the procedure that for every k consecutive observations, one is kept, the rest being skipped, and recently some advances have been made in causal discovery from such data. With temporal aggregation, the local averages or sums of k consecutive, non-overlapping observations in the causal process are computed as new observations, and causal discovery from such data is even harder. In this paper, we investigate how to recover causal relations at the original causal frequency from temporally aggregated data when k is known. Assuming the time series at the causal frequency follows a vector autoregressive (VAR) model, we show that the causal structure at the causal frequency is identifiable from aggregated time series if the noise terms are independent and non-Gaussian and some other technical conditions hold. We then present an estimation method based on non-Gaussian state-space modeling and evaluate its performance on both synthetic and real data.