ABC-based Forecasting in State Space Models

TL;DR

This paper explores using Approximate Bayesian Computation (ABC) for probabilistic forecasting in state space models, especially under model misspecification, and introduces focused Bayesian prediction methods that improve forecast accuracy.

Contribution

It investigates ABC-based forecasting in misspecified state space models and introduces focused prediction methods driven by scoring rules to enhance forecast accuracy.

Findings

Focused methods outperform traditional predictive approaches.

Predictions align well with chosen scoring rules in simulations.

Empirical application demonstrates practical effectiveness.

Abstract

Approximate Bayesian Computation (ABC) has gained popularity as a method for conducting inference and forecasting in complex models, most notably those which are intractable in some sense. In this paper we use ABC to produce probabilistic forecasts in state space models (SSMs). Whilst ABC-based forecasting in correctly-specified SSMs has been studied, the misspecified case has not been investigated, and it is that case which we emphasize. We invoke recent principles of 'focused' Bayesian prediction, whereby Bayesian updates are driven by a scoring rule that rewards predictive accuracy; the aim being to produce predictives that perform well in that rule, despite misspecification. Two methods are investigated for producing the focused predictions. In a simulation setting, 'coherent' predictions are in evidence for both methods: the predictive constructed via the use of a particular scoring rule predicts best according to that rule. Importantly, both focused methods typically produce more accurate forecasts than an exact, but misspecified, predictive. An empirical application to a truly intractable SSM completes the paper.