Developed as a refinement of stochastic volatility (SV) models, the stochastic volatility in mean (SVM) model incorporates the latent volatility as an explanatory variable in both the mean and variance equations. It, therefore, provides a way of assessing the relationship between returns and volatility, albeit at the expense of complicating the estimation process. This study introduces a Bayesian methodology that leverages data-cloning algorithms to obtain maximum likelihood estimates for SV and SVM model parameters. Adopting this Bayesian framework allows approximate maximum likelihood estimates to be attained without the need to maximize pseudo likelihood functions. The key contribution this paper makes is that it proposes an estimator for the SVM model, one that uses Bayesian algorithms to approximate the maximum likelihood estimate with great effect. Notably, the estimates it provides yield superior outcomes than those derived from the Markov chain Monte Carlo (MCMC) method in terms of standard errors, all while being unaffected by the selection of prior distributions.

中文翻译：

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测试数据克隆作为均值模型随机波动估计器的基础

均值随机波动率 (SVM) 模型是作为随机波动率 (SV) 模型的改进而开发的，将潜在波动率作为均值和方差方程中的解释变量。因此，它提供了一种评估回报与波动性之间关系的方法，尽管代价是使估计过程变得复杂。本研究引入了贝叶斯方法，该方法利用数据克隆算法来获得 SV 和 SVM 模型参数的最大似然估计。采用这种贝叶斯框架可以实现近似最大似然估计，而无需最大化伪似然函数。本文的主要贡献是提出了 SVM 模型的估计器，一种使用贝叶斯算法来近似最大似然估计的方法，效果很好。值得注意的是，就标准误差而言，它提供的估计产生的结果优于马尔可夫链蒙特卡罗 (MCMC) 方法得出的结果，同时不受先验分布选择的影响。