State space models (SSMs) are widely used to describe dynamic systems. However, when the likelihood of the observations is intractable, parameter inference for SSMs cannot be easily carried out using standard Markov chain Monte Carlo or sequential Monte Carlo methods. In this paper, we propose a particle Gibbs sampler as a general strategy to handle SSMs with intractable likelihoods in the approximate Bayesian computation (ABC) setting. The proposed sampler incorporates a conditional auxiliary particle filter, which can help mitigate the weight degeneracy often encountered in ABC. To illustrate the methodology, we focus on a classic stochastic volatility model (SVM) used in finance and econometrics for analyzing and interpreting volatility. Simulation studies demonstrate the accuracy of our sampler for SVM parameter inference, compared to existing particle Gibbs samplers based on the conditional bootstrap filter. As a real data application, we apply the proposed sampler for fitting an SVM to S&P 500 Index time-series data during the 2008 financial crisis.

翻译：状态空间模型（SSMs）被广泛用于描述动态系统。然而，当观测似然函数难以处理时，无法轻易使用标准马尔可夫链蒙特卡洛或序贯蒙特卡洛方法进行SSM的参数推断。本文提出一种粒子吉布斯采样器，作为在近似贝叶斯计算框架下处理具有难处理似然函数的SSM的通用策略。该采样器引入条件辅助粒子滤波，有助于缓解ABC中常见的权重退化问题。为阐述该方法，我们聚焦于金融计量经济学中用于分析与解释波动率的经典随机波动率模型（SVM）。仿真研究表明，与基于条件自助滤波器的现有粒子吉布斯采样器相比，所提采样器在SVM参数推断中具有更高的准确性。在实际数据应用中，我们将所提采样器用于拟合2008年金融危机期间标普500指数时间序列数据的SVM。