TimeGDC: Towards Efficient and Robust Joint Distribution Learning for Long-Term Probabilistic Time Series Forecasting

Traditional point-based time series forecasting provides limited information for risk-aware decision-making. Long-term probabilistic forecasting methods, however, often suffer from low computational efficiency and limited robustness, especially when dealing with complex distributions and potentially contaminated observations over extended forecast horizons. To address these challenges, we propose TimeGDC, a contamination-aware framework for efficient joint probabilistic forecasting over long horizons. TimeGDC jointly models the predictive distribution over the entire forecasting horizon using a Gaussian mixture distribution that captures multimodal uncertainty. Each mixture component is parameterized with a Dynamically smoothed low-rank covariance structure to efficiently represent temporal dependencies among future time steps. Furthermore, we construct a Contamination-aware likelihood for joint forecasting by combining the predictive distribution with a fixed heavy-tailed reference distribution, thereby reducing the influence of abnormal observations on distribution learning. Extensive experiments on six widely used multivariate time-series benchmark datasets show that TimeGDC consistently outperforms four competitive probabilistic forecasting baselines, achieving average relative reductions of 16.6%, 7.7%, and 13.4% in CRPS, NMAE, and Energy Score, respectively.