Hidden Markov graphical models with state-dependent generalized hyperbolic distributions

ArXiv ID: 2412.03668 “View on arXiv”

Authors: Unknown

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.

Keywords: Hidden Markov Graphical Model, Generalized Hyperbolic Distributions, L1 Penalty (Sparse Precision Matrices), Penalized EM Algorithm, Time-varying Interconnectedness, Multi-Asset (Indices, Crypto, Commodities)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced statistical techniques including generalized hyperbolic distributions, location-scale mixture representations, and penalized EM algorithms, demonstrating high mathematical complexity. It validates the methodology through simulation studies and applies it to real-world financial data (indices, cryptocurrencies, commodities) over a defined period, showing strong empirical rigor.

  flowchart TD
    A["Research Goal<br>Model Time-varying Market Interconnectedness<br>under Dynamic, Heavy-tailed Conditions"] --> B["Methodology: Hidden Markov Graphical Model<br>with State-dependent Generalized Hyperbolic Distributions"]
    B --> C["Computational Process<br>Penalized EM Algorithm<br>(L1 Penalty for Sparse Precision Matrices)"]
    C --> D["Simulation Validation<br>Test Model Recovery under Various Scenarios"]
    C --> E["Empirical Application<br>Daily Returns (2017-2023)<br>Indices, Crypto, Commodities"]
    D --> F["Key Outcomes"]
    E --> F
    F --> G["Regime-specific Conditional Correlation Graphs"]
    F --> H["Identification of Time-varying Network Connectivity"]