Probabilistic Forecasting with VAR-VAE: Advancing Time Series Forecasting under Uncertainty

Abstract

We introduce the VAR-VAE, a novel time series model that combines the generative capabilities of Variational Autoencoders (VAEs) with Vector Autoregression (VAR) models in the latent space. The VAR-VAE encodes noisy time series into a first-lag VAR probabilistic latent space. We show that this improves the forecasting performance and reduces overfitting, especially at high noise-to-signal ratios. We also show that, compared to a traditional CNN-LSTM model, the VAR-VAE yields a 3–10% reduction in MSE, while converging in 66% fewer training epochs. Furthermore, we also show how the model's probabilistic forecasts can improve practical decision-making under uncertainty. In simulated securities trading scenarios using model-derived confidence, the VAR-VAE achieves higher Sharpe Ratios and greater directional accuracy compared to using point estimates. These results highlight the model's effectiveness in practical applications, especially in environments with noisy data. Future research may focus on extending VAR-VAE to multi-step forecasting or incorporating more advanced latent structures, such as VARMA models.