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. The study aims to forecast returns of a 40-dimensional time series of stock data on the Johannesburg Stock Exchange using SGDLMs. The SGDLM approach involves constructing a customised dynamic linear model (DLM) for each univariate time series. Every day, the DLMs are recoupled using importance sampling and decoupled using mean-field variational Bayes. Our results suggest that SGDLMs forecast the stock data accurately and respond to market gyrations nicely. Teams Link