Dynamic Skewness in Stochastic Volatility Models: A Penalized Prior Approach

ArXiv ID: 2508.10778 “View on arXiv”

Authors: Bruno E. Holtz, Ricardo S. Ehlers, Adriano K. Suzuki, Francisco Louzada

Abstract

Financial time series often exhibit skewness and heavy tails, making it essential to use models that incorporate these characteristics to ensure greater reliability in the results. Furthermore, allowing temporal variation in the skewness parameter can bring significant gains in the analysis of this type of series. However, for more robustness, it is crucial to develop models that balance flexibility and parsimony. In this paper, we propose dynamic skewness stochastic volatility models in the SMSN family (DynSSV-SMSN), using priors that penalize model complexity. Parameter estimation was carried out using the Hamiltonian Monte Carlo (HMC) method via the \texttt{“RStan”} package. Simulation results demonstrated that penalizing priors present superior performance in several scenarios compared to the classical choices. In the empirical application to returns of cryptocurrencies, models with heavy tails and dynamic skewness provided a better fit to the data according to the DIC, WAIC, and LOO-CV information criteria.

Keywords: Dynamic skewness stochastic volatility, Hamiltonian Monte Carlo, Heavy tails, SMSN family, Cryptocurrency returns, Cryptocurrency

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 8.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced Bayesian statistics with Hamiltonian Monte Carlo, complex skew-normal/Student-t distributions, and penalized complexity priors, indicating high mathematical density. It also presents rigorous empirical validation using simulation studies, information criteria (DIC, WAIC, LOO-CV), and application to real cryptocurrency data, demonstrating strong implementation and backtesting readiness.

  flowchart TD
    A["Research Goal<br>Dynamic skewness in stochastic volatility models<br>with penalized priors for robustness"] --> B["Methodology<br>Propose DynSSV-SMSN models<br>using penalized priors"]
    B --> C["Computation<br>Parameter estimation via HMC<br>using RStan package"]
    C --> D["Simulation<br>Test penalized vs. classical priors<br>across multiple scenarios"]
    C --> E["Empirical Analysis<br>Cryptocurrency returns data<br>heavy tails & dynamic skewness"]
    D --> F["Key Findings<br>Penalized priors: Superior performance<br>Empirical: Better fit via DIC, WAIC, LOO-CV"]
    E --> F