Generative models with helical time encoding for seasonal time series forecasting

Many time series forecasting methods rely on sliding windows of historical data. The window size is one of the hyperparameters that significantly influences predictive accuracy, yet optimal selection remains challenging in practice. We propose an encoding of time that, when used with generative models, transforms the seasonal time series forecasting problem into a conditional generation problem on a helical representation. This representation allows models to learn position-value relationships rather than sequential dependencies, enabling forecasting using only time-derived conditions, thereby eliminating the need for sliding windows and recent observations during inference while fully exploiting historical patterns during training. We evaluated our approach using conditional Generative Adversarial Networks on taxi demand and influenza-like illness forecasting benchmarks. Our model demonstrated substantial improvements over state-of-the-art baselines in long-term forecasting scenarios. For influenza-like illness forecasting, we achieved a 42.2% mean absolute error reduction (from 1.1378 to 0.6582) and a 35.3% root mean square error reduction (from 1.3063 to 0.8453) compared to baseline models using only historical data for long-term predictions. For taxi demand forecasting, we achieved a 70.7% root mean square error reduction (from 0.7926 to 0.2322) compared to baseline models using recent observations during inference. Our approach provides a specialized solution for seasonal time series forecasting, presenting advantages when long-term predictions are required without waiting for new actual data or in high-frequency applications where continuous re-computation is expensive.