论文标题
关于Beta-Bartlett和Uhlig扩展过程之间的关系
On the relationship between beta-Bartlett and Uhlig extended processes
论文作者
论文摘要
随机波动过程用于多元时间序列分析中，以跟踪协方差矩阵中的时变模式。 uhlig扩展和β-巴特利特流程对于分析高维时序特别方便，因为它们与WishArt的可能性是共轭的。在本文中，我们表明uhlig扩展和β-bartlett密切相关，但不是等效的：它们的超参数可以匹配，以便它们具有相同的前向过滤后的后代和一步的预测，但后面的（平滑）后部分布不同。在这种情况下，贝叶斯因素无法区分模型，并且需要进行模型比较的替代方法。我们在回顾性汇率回报率的回顾性分析中说明了这些问题。此外，我们为Beta-Bartlett过程提供了一种向后的采样算法，为此尚未开发回顾性分析。
Stochastic volatility processes are used in multivariate time-series analysis to track time-varying patterns in covariance matrices. Uhlig extended and beta-Bartlett processes are especially convenient for analyzing high-dimensional time-series because they are conjugate with Wishart likelihoods. In this article, we show that Uhlig extended and beta-Bartlett are closely related, but not equivalent: their hyperparameters can be matched so that they have the same forward-filtered posteriors and one-step ahead forecasts, but different joint (smoothed) posterior distributions. Under this circumstance, Bayes factors can't discriminate the models and alternative approaches to model comparison are needed. We illustrate these issues in a retrospective analysis of volatilities of returns of foreign exchange rates. Additionally, we provide a backward sampling algorithm for the beta-Bartlett process, for which retrospective analysis had not been developed.
