  Cross-series dependencies are crucial in obtaining accurate forecasts when
forecasting a multivariate time series. Simultaneous Graphical Dynamic Linear
Models (SGDLMs) are Bayesian models that elegantly capture cross-series
dependencies. This study forecasts returns of a 40-dimensional time series of
stock data from the Johannesburg Stock Exchange (JSE) using SGDLMs. The SGDLM
approach involves constructing a customised dynamic linear model (DLM) for each
univariate time series. At each time point, the DLMs are recoupled using
importance sampling and decoupled using mean-field variational Bayes. Our
results suggest that SGDLMs forecast stock data on the JSE accurately and
respond to market gyrations effectively.
