Hamiltonian Monte Carlo

Centered MA Dirichlet ARMA for Financial Compositions: Theory & Empirical Evidence ArXiv ID: 2510.18903 “View on arXiv” Authors: Harrison Katz Abstract Observation-driven Dirichlet models for compositional time series commonly use the additive log-ratio (ALR) link and include a moving-average (MA) term based on ALR residuals. In the standard Bayesian Dirichlet Auto-Regressive Moving-Average (B-DARMA) recursion, this MA regressor has a nonzero conditional mean under the Dirichlet likelihood, which biases the mean path and complicates interpretation of the MA coefficients. We propose a minimal change: replace the raw regressor with a centered innovation equal to the ALR residual minus its conditional expectation, computable in closed form using digamma functions. Centering restores mean-zero innovations for the MA block without altering either the likelihood or the ALR link. We provide closed-form identities for the conditional mean and forecast recursion, show first-order equivalence to a digamma-link DARMA while retaining a simple inverse back to the mean composition, and supply ready-to-use code. In a weekly application to the Federal Reserve H.8 bank-asset composition, the centered specification improves log predictive scores with virtually identical point accuracy and markedly cleaner Hamiltonian Monte Carlo diagnostics. ...

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. ...

Realized Local Volatility Surface ArXiv ID: 2504.15626 “View on arXiv” Authors: Unknown Abstract For quantitative trading risk management purposes, we present a novel idea: the realized local volatility surface. Concisely, it stands for the conditional expected volatility when sudden market behaviors of the underlying occur. One is able to explore risk management usages by following the orthotical Delta-Gamma dynamic hedging framework. The realized local volatility surface is, mathematically, a generalized Wiener measure from historical prices. It is reconstructed via employing high-frequency trading market data. A Stick-Breaking Gaussian Mixture Model is fitted via Hamiltonian Monte Carlo, producing a local volatility surface with 95% credible intervals. A practically validated Bayesian nonparametric estimation workflow. Empirical results on TSLA high-frequency data illustrate its ability to capture counterfactual volatility. We also discuss its application in improving volatility-based risk management. ...