Bridging Time and Frequency: A Joint Modeling Framework for Irregular Multivariate Time Series Forecasting

TL;DR

This work tackles irregular multivariate time series forecasting by bridging time and frequency, introducing TFMixer, a joint modeling framework. It combines a Global Frequency Module with a learnable NUDFT to extract spectral information directly from irregular timestamps and a Local Time Module with a query-based patch mechanism to capture fine-grained temporal dynamics, then fuses these signals and refines seasonal bias via inverse NUDFT. The model is trained with a joint forecasting and reconstruction loss to ensure both accurate predictions and faithful spectral representations, enabling explicit seasonal extrapolation. Across PhysioNet, MIMIC, HumanActivity, and USHCN, TFMixer achieves state-of-the-art results and demonstrates robust cross-domain generalization, validating the effectiveness of decoupled time–frequency modeling for irregular data.

Abstract

Irregular multivariate time series forecasting (IMTSF) is challenging due to non-uniform sampling and variable asynchronicity. These irregularities violate the equidistant assumptions of standard models, hindering local temporal modeling and rendering classical frequency-domain methods ineffective for capturing global periodic structures. To address this challenge, we propose TFMixer, a joint time-frequency modeling framework for IMTS forecasting. Specifically, TFMixer incorporates a Global Frequency Module that employs a learnable Non-Uniform Discrete Fourier Transform (NUDFT) to directly extract spectral representations from irregular timestamps. In parallel, the Local Time Module introduces a query-based patch mixing mechanism to adaptively aggregate informative temporal patches and alleviate information density imbalance. Finally, TFMixer fuses the time-domain and frequency-domain representations to generate forecasts and further leverages inverse NUDFT for explicit seasonal extrapolation. Extensive experiments on real-world datasets demonstrate the state--of-the-art performance of TFMixer.

Figures (10)

• Figure 1: The comparison of irregular multivariate time series forecasting (a) and regular multivariate time series forecasting (b).
• Figure 2: Global and local temporal dependencies in IMTSF. The observed time points (green dots) are sampled non-uniformly, creating challenges for traditional models. The global periodicity (blue dashed line) represents long-range seasonal patterns, while local dependencies (pink shaded area) capture fine-grained temporal dynamics within specific intervals.
• Figure 3: TFMixer architecture. (1) Masked RevIN Module normalizes/denormalizes the data. (2) Global Frequency Module captures long-range periodic dependencies through a learnable Non-Uniform Discrete Fourier Transform (NUDFT). (3) Local Time Module extracts fine-grained patterns using a transformable patch encoder followed by query-based attention and dual-mixing blocks. (4) Output Module performs joint time-frequency feature fusion to generate the final forecasting results.
• Figure 4: Parameter sensitivity studies of TFMixer, analyzing the impact of different model dimensions D.
• Figure 5: Parameter sensitivity studies of TFMixer, analyzing the impact of different number of learnable query patches W.