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

TL;DR

TimeGMM introduces a single-pass probabilistic forecasting method using adaptive Gaussian Mixture Models with reversible normalization, effectively capturing complex distributions and outperforming existing approaches in energy and finance applications.

Contribution

The paper proposes TimeGMM, a novel framework combining GMM, reversible normalization, and specialized modules for dynamic, accurate probabilistic time series forecasting.

Findings

Outperforms state-of-the-art methods in CRPS and NMAE metrics.

Effectively models complex future distributions in a single forward pass.

Demonstrates robustness across diverse energy and finance datasets.

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.