Hierarchical modeling of multiple synchronized irregularly spaced financial returns

ABSTRACT Intraday transaction‐level data on financial assets constitute high‐frequency, irregularly spaced time series, posing challenges for volatility modeling. Traditional stochastic volatility models, designed for regularly spaced time series, are not directly applicable in this setting. This paper introduces two hierarchical Bayesian models—the irregular basic multivariate stochastic volatility autoregressive conditional duration model and the irregular dynamic multivariate stochastic volatility autoregressive conditional duration model to address these challenges and effectively model volatility in irregular intra‐day data. These models incorporate the autoregressive conditional duration model to account for irregular gaps between transactions, improving the understanding of market microstructure and future dynamics. The analysis is conducted within a Bayesian framework using the Hamiltonian Monte Carlo algorithm with No‐U‐turn sampler in R via the cmdstanr package. We demonstrate the efficacy of our methodology through simulation studies and an illustrative example using intra‐day prices of healthcare stocks traded on the New York Stock Exchange at the microsecond level. Utilizing the refresh time sampling technique, we synchronize transactions, compute synchronized log‐returns and gaps, and use these for modeling purposes.