AUTHOR=Sigauke Caston , Moroke Ntebogang , Makatjane Katleho , Shoko Claris 

TITLE=A deep learning forecasting of downside risk: application of a combined ESRNN-VAE

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 11 - 2025

YEAR=2025

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2025.1662252

DOI=10.3389/fams.2025.1662252

ISSN=2297-4687

ABSTRACT=IntroductionTraditional time-series models such as the ARIMA and the Generalized Autoregressive Conditional Heteroscedasticity depend nonlinear dynamics and stationarity, limiting their ability to model nonlinear relationships and sudden regime changes.MethodsThis research introduces a combined forecasting model that uses the clear structure of an Exponential Smoothing Recurrent Neural Network and the creative features of a Variational Autoencoder to predict the risk of falling stock prices for Sasol Limited from 2010 to 2025. The model seeks to find long-term trends and short-term changes in the value of stocks linked to commodities, which can face big losses due to political events, changes in oil prices, and shifts in climate policies.ResultsA weighted combination of the deterministic ESRNN, which gets 60% of the weight, and the stochastic VAE, which gets 40%, shows strong accuracy in predicting stock prices over short, medium, and long periods. Shapley value analysis identifies 24-day lags, investor sentiment, oil prices, the 2015/2016 Shanghai Stock Exchange crash, the Russia-Ukraine war, and South African monetary policy news as the primary predictors of downside risk. The model effectively quantifies essential tail risk metrics, such as Maximum Drawdown, Sortino Ratio, and Marginal Expected Shortfall. A 99% prediction interval width (PIW) of 3.4398 indicates the model's reliability in capturing extreme events and uncertainty during turbulent periods.DiscussionThe results indicate the model's robustness and practical utility as a decision-support tool for risk-aware forecasting in resource-dependent financial markets.