Combined parameter and state inference with automatically calibrated ABC
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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 ϵ. We construct an algorithm, which performs this inference, that automatically calibrates ϵ 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.
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