Hidden Markov graphical models with state-dependent generalized hyperbolic distributions

TL;DR

This paper introduces a hidden Markov graphical model with generalized hyperbolic distributions to analyze dynamic interconnectedness in financial markets, capturing regime shifts and network structures over time.

Contribution

It develops a novel model combining hidden Markov processes with generalized hyperbolic distributions and a penalized EM algorithm for sparse precision matrix estimation in financial data.

Findings

Identifies regime-specific network connectivity patterns.

Effectively captures time-varying correlations in financial markets.

Validates approach through simulation and empirical data analysis.

Abstract

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.