Combined parameter and state inference with automatically calibrated ABC

Abstract

State space models contain time-indexed parameters, called states; some also contain fixed parameters, or simply parameters. The combined problem of fixed parameter and state inference, based on some time-indexed observations, has been the subject of much recent literature. Applying combined parameter and state inference techniques to state space models with intractable likelihoods requires extensive manual calibration of a time-indexed tuning parameter, the ABC distance threshold \(\epsilon\). We construct an algorithm, which performs this inference, that automatically calibrates \(\epsilon\) as it progresses through the observations. There are no other time-indexed tuning parameters. We demonstrate this algorithm with three examples: a simulated example of skewed normal distributions, an inhomogenous Hawkes process, and an econometric volatility model.