Reliable estimates of volatility and correlation are fundamental in economics and finance for understanding the impact of macroeconomics events on the market and guiding future investments and policies. Dependence across financial returns is likely to be subject to sudden structural changes, especially in correspondence with major global events, such as the COVID-19 pandemic. In this work, we are interested in capturing abrupt changes over time in the dependence across US industry stock portfolios, over a time horizon that covers the COVID-19 pandemic. The selected stocks give a comprehensive picture of the US stock market. To this end, we develop a Bayesian multivariate stochastic volatility model based on a time-varying sequence of graphs capturing the evolution of the dependence structure. The model builds on the Gaussian graphical models and the random change points literature. In particular, we treat the number, the position of change points, and the graphs as object of posterior inference, allowing for sparsity in graph recovery and change point detection. The high dimension of the parameter space poses complex computational challenges. However, the model admits a hidden Markov model formulation. This leads to the development of an efficient computational strategy, based on a combination of sequential Monte-Carlo and Markov chain Monte-Carlo techniques. Model and computational development are widely applicable, beyond the scope of the application of interest in this work.

翻译：波动性和相关性的可靠估计是经济学和金融学中理解宏观经济事件对市场影响、指导未来投资和政策的基础。金融收益之间的依存关系容易发生突然的结构性变化，尤其是在COVID-19疫情等重大全球事件期间。本研究聚焦于捕捉涵盖COVID-19疫情的时间范围内，美国行业股票投资组合之间依存关系的突变。所选取的股票全面反映了美国股市的整体情况。为此，我们开发了一种基于时变图序列的贝叶斯多元随机波动模型，该序列可捕捉依存结构的演变。该模型建立在高斯图模型和随机变点文献的基础上。具体而言，我们将变点的数量、位置以及图视为后验推断的对象，从而在图的恢复和变点检测中实现稀疏性。参数空间的高维性带来了复杂的计算挑战。然而，该模型可转化为隐马尔可夫模型形式。基于此，我们结合序贯蒙特卡洛和马尔可夫链蒙特卡洛技术，开发了一种高效的计算策略。该模型及计算方法具有广泛适用性，超出了本文具体应用的范围。