  Simulation models often lack tractable likelihood functions, making
likelihood-free inference methods indispensable. Approximate Bayesian
computation generates likelihood-free posterior samples by comparing simulated
and observed data through some distance measure, but existing approaches are
often poorly suited to time series simulators, for example due to an
independent and identically distributed data assumption. In this paper, we
propose to use path signatures in approximate Bayesian computation to handle
the sequential nature of time series. We provide theoretical guarantees on the
resultant posteriors and demonstrate competitive Bayesian parameter inference
for simulators generating univariate, multivariate, irregularly spaced, and
even non-Euclidean sequences.
