Bayesian Inference for Stochastic Volatility Models Using Non-Gaussian Ornstein-Uhlenbeck Process Superposition

This article presents source code that performs Bayesian inference for stochastic volatility models using continuous superposition of non-Gaussian Ornstein-Uhlenbeck processes. To enhance understanding, let's clarify these technical terms: Non-Gaussian indicates that data distributions deviate from normal distributions, requiring specialized statistical methods for handling leptokurtic or skewed financial returns. The Ornstein-Uhlenbeck process serves as a mathematical framework for modeling mean-reverting stochastic processes commonly used in financial volatility modeling. Continuous superposition involves combining multiple model components through integration techniques to improve forecasting accuracy. Bayesian inference provides a probabilistic framework for parameter estimation that combines prior knowledge with observed data through Markov Chain Monte Carlo (MCMC) sampling algorithms. The implementation likely leverages hierarchical Bayesian modeling with latent volatility states, where key functions may include density estimation for non-Gaussian innovations, Kalman-filter-like recursion for state updates, and Metropolis-Hastings algorithms for posterior sampling. Through these technical clarifications, we aim to make the article more accessible while helping readers grasp the core methodologies involved in advanced volatility modeling.