Time-Varying Stochastic Graph Learning for Probabilistic Financial Forecasting

Financial forecasting involves both time-varying interactions among market variables and substantial uncertainty, yet these two features are often modeled separately or through fixed relational structures. This study develops a time-varying stochastic graph framework that jointly learns dynamic financial connectivity and probabilistic forecasts. The empirical application uses 2,544 daily observations from January 2015 to July 2026 for the Straits Times Index (STI), USD/SGD exchange rate, VIX, and S&P 500. A state-dependent stochastic graph is learned from the observed financial variables, and the resulting graph representations are processed by a long short-term memory network to estimate the conditional mean and standard deviation of next-day STI returns. Out-of-sample results show only marginal improvements in point forecasting over a random-walk benchmark, with directional accuracy of 50.8%. In contrast, the model produces time-varying graph connectivity and reasonably calibrated predictive intervals, with empirical coverage of 84.6% and 93.7% for the nominal 80% and 95% intervals, respectively.