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Hidden Markov graphical models with state-dependent generalized hyperbolic distributions

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  • Beatrice Foroni
  • Luca Merlo
  • Lea Petrella

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.

Suggested Citation

  • Beatrice Foroni & Luca Merlo & Lea Petrella, 2024. "Hidden Markov graphical models with state-dependent generalized hyperbolic distributions," Papers 2412.03668, arXiv.org.
  • Handle: RePEc:arx:papers:2412.03668
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    References listed on IDEAS

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    5. Bouri, Elie & Molnár, Peter & Azzi, Georges & Roubaud, David & Hagfors, Lars Ivar, 2017. "On the hedge and safe haven properties of Bitcoin: Is it really more than a diversifier?," Finance Research Letters, Elsevier, vol. 20(C), pages 192-198.
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    7. Corbet, Shaen & Meegan, Andrew & Larkin, Charles & Lucey, Brian & Yarovaya, Larisa, 2018. "Exploring the dynamic relationships between cryptocurrencies and other financial assets," Economics Letters, Elsevier, vol. 165(C), pages 28-34.
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