英文标题：
《A Bayesian GED-Gamma stochastic volatility model for return data: a
  marginal likelihood approach》
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作者：
T. R. Santos
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最新提交年份：
2018
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英文摘要：
  Several studies explore inferences based on stochastic volatility (SV) models, taking into account the stylized facts of return data. The common problem is that the latent parameters of many volatility models are high-dimensional and analytically intractable, which means inferences require approximations using, for example, the Markov Chain Monte Carlo or Laplace methods. Some SV models are expressed as a linear Gaussian state-space model that leads to a marginal likelihood, reducing the dimensionality of the problem. Others are not linearized, and the latent parameters are integrated out. However, these present a quite restrictive evolution equation. Thus, we propose a Bayesian GED-Gamma SV model with a direct marginal likelihood that is a product of the generalized Student\'s t-distributions in which the latent states are related across time through a stationary Gaussian evolution equation. Then, an approximation is made for the prior distribution of log-precision/volatility, without the need for model linearization. This also allows for the computation of the marginal likelihood function, where the high-dimensional latent states are integrated out and easily sampled in blocks using a smoothing procedure. In addition, extensions of our GED-Gamma model are easily made to incorporate skew heavy-tailed distributions. We use the Bayesian estimator for the inference of static parameters, and perform a simulation study on several properties of the estimator. Our results show that the proposed model can be reasonably estimated. Furthermore, we provide case studies of a Brazilian asset and the pound/dollar exchange rate to show the performance of our approach in terms of fit and prediction.   Keywords: SV model, New sequential and smoothing procedures, Generalized Student\'s t-distribution, Non-Gaussian errors, Heavy tails, Skewness
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中文摘要：
一些研究探讨了基于随机波动率（SV）模型的推断，并考虑了回报数据的程式化事实。常见的问题是，许多波动率模型的潜在参数都是高维且难以分析的，这意味着推断需要使用马尔可夫链蒙特卡罗或拉普拉斯方法进行近似。一些SV模型表示为线性高斯状态空间模型，该模型导致边际可能性，从而降低了问题的维数。其他参数没有线性化，潜在参数被积分出来。然而，这些提出了一个相当严格的进化方程。因此，我们提出了一个贝叶斯GED Gamma SV模型，该模型具有直接的边际似然，该似然是广义Student t分布的乘积，其中潜态通过平稳的高斯演化方程随时间相关。然后，对对数精度/波动率的先验分布进行近似，无需模型线性化。这也允许计算边际似然函数，其中高维潜在状态被积分出来，并使用平滑程序轻松地在块中采样。此外，我们的GED Gamma模型的扩展很容易合并斜重尾分布。我们使用贝叶斯估计器来推断静态参数，并对估计器的几个性质进行了仿真研究。我们的结果表明，所提出的模型是可以合理估计的。此外，我们还提供了巴西资产和英镑/美元汇率的案例研究，以显示我们的方法在拟合和预测方面的性能。关键词：SV模型、新的序列和平滑程序、广义Student t分布、非高斯误差、重尾、偏态
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Statistics        统计学
二级分类：Other Statistics        其他统计数字
分类描述：Work in statistics that does not fit into the other stat classifications
从事不适合其他统计分类的统计工作
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