In this paper we consider the simulation-based Bayesian analysis of stochastic volatility in mean (SVM) models. Extending the highly efficient Markov chain Monte Carlo mixture sampler for the SV model proposed in Kim et al. (1998) and Omori et al. (2007), we develop an accurate approximation of the non-central chi-squared distribution as a mixture of thirty normal distributions. Under this mixture representation, we sample the parameters and latent volatilities in one block. We also detail a correction of the small approximation error by using additional Metropolis-Hastings steps. The proposed method is extended to the SVM model with leverage. The methodology and models are applied to excess holding yields in empirical studies, and the SVM model with leverage is shown to outperform competing volatility models based on marginal likelihoods.

翻译：本文研究了基于模拟的贝叶斯分析方法在均值随机波动模型中的应用。通过扩展Kim等人（1998）及Omori等人（2007）提出的针对SV模型的高效马尔可夫链蒙特卡洛混合抽样器，我们开发了一种将非中心卡方分布近似为三十个正态分布混合的精确方法。在此混合表示下，我们实现了参数与潜在波动率的一次性块抽样。同时，我们详细阐述了通过附加Metropolis-Hastings步骤对微小近似误差进行校正的方法。所提方法进一步扩展至含杠杆效应的SVM模型。在实证研究中，我们将该方法与模型应用于超额持有期收益率，并基于边际似然性证明，含杠杆效应的SVM模型优于其他竞争性波动率模型。