  We propose a heterogeneous simultaneous graphical dynamic linear model
(H-SGDLM), which extends the standard SGDLM framework to incorporate a
heterogeneous autoregressive realised volatility (HAR-RV) model. This novel
approach creates a GPU-scalable multivariate volatility estimator, which
decomposes multiple time series into economically-meaningful variables to
explain the endogenous and exogenous factors driving the underlying
variability. This unique decomposition goes beyond the classic one step ahead
prediction; indeed, we investigate inferences up to one month into the future
using stocks, FX futures and ETF futures, demonstrating its superior
performance according to accuracy of large moves, longer-term prediction and
consistency over time.
