TimeGMM: Single-Pass Probabilistic Forecasting via Adaptive Gaussian Mixture Models with Reversible Normalization

Abstract: Probabilistic time series forecasting is crucial for quantifying future uncertainty, with significant applications in fields such as energy and finance. However, existing methods often rely on computationally expensive sampling or restrictive parametric assumptions to characterize future distributions, which limits predictive performance and introduces distributional mismatch. To address these challenges, this paper presents TimeGMM, a novel probabilistic forecasting framework based on Gaussian Mixture Models (GMM) that captures complex future distributions in a single forward pass. A key component is GMM-adapted Reversible Instance Normalization (GRIN), a novel module designed to dynamically adapt to temporal-probabilistic distribution shifts. The framework integrates a dedicated Temporal Encoder (TE-Module) with a Conditional Temporal-Probabilistic Decoder (CTPD-Module) to jointly capture temporal dependencies and mixture distribution parameters. Extensive experiments demonstrate that TimeGMM consistently outperforms state-of-the-art methods, achieving maximum improvements of 22.48\% in CRPS and 21.23\% in NMAE.