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.

翻译：近似贝叶斯计算（ABC）作为一种在复杂模型（尤其是某些意义上难以处理的模型）中进行推断和预测的方法，已获得广泛关注。本文利用ABC在状态空间模型（SSM）中生成概率预测。虽然基于ABC的正确设定SSM预测已有研究，但错误设定情形尚未被探究，这正是本文的重点。我们借鉴了近期提出的"聚焦"贝叶斯预测原理，其中贝叶斯更新由奖励预测准确性的评分规则驱动；其目标是在错误设定情况下，仍能生成在该规则下表现良好的预测结果。本文研究了两种生成聚焦预测的方法。在模拟设置中，两种方法均呈现"一致性"预测特征：通过特定评分规则构建的预测在该规则下表现最优。重要的是，两种聚焦方法通常比精确但错误设定的预测能产生更准确的预测结果。本文最终通过一个真正难以处理的SSM实证应用完成全篇研究。