In this paper we develop a novel hidden Markov graphical model to investigate time-varying interconnectedness between different financial markets. To identify conditional correlation structures under varying market conditions and accommodate stylized facts embedded in financial time series, we rely upon the generalized hyperbolic family of distributions with time-dependent parameters evolving according to a latent Markov chain. We exploit its location-scale mixture representation to build a penalized EM algorithm for estimating the state-specific sparse precision matrices by means of an $L_1$ penalty. The proposed approach leads to regime-specific conditional correlation graphs that allow us to identify different degrees of network connectivity of returns over time. The methodology's effectiveness is validated through simulation exercises under different scenarios. In the empirical analysis we apply our model to daily returns of a large set of market indexes, cryptocurrencies and commodity futures over the period 2017-2023.

翻译：本文提出了一种新颖的隐马尔可夫图模型，用于研究不同金融市场之间的时变关联性。为识别不同市场条件下的条件相关结构，并适应金融时间序列中存在的典型化事实，我们采用参数随时间变化的广义双曲分布族，其参数通过隐马尔可夫链演化。利用该分布的位置-尺度混合表示，我们构建了一种惩罚性EM算法，通过$L_1$惩罚项估计状态特定的稀疏精度矩阵。所提出的方法能够生成机制特定的条件相关图，从而识别收益率网络连接度随时间变化的不同程度。通过不同场景下的模拟实验验证了该方法的有效性。在实证分析中，我们将模型应用于2017-2023年间大量市场指数、加密货币和大宗商品期货的日收益率数据。