Hidden Markov graphical models with state‐dependent generalized hyperbolic distributions

Abstract In this article, 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 shape features 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 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 indices, cryptocurrencies and commodity futures over the period 2017–2023.