Are Time-Indexed Foundation Models the Future of Time Series Imputation?
Etienne Le Naour, Tahar Nabil, Adrien Petralia, Ghislain Agoua
TL;DR
The paper tackles zero-shot imputation for irregular time series by evaluating time-indexed foundation models, specifically MoTM and TabPFN-TS, which produce continuous-time representations $H(t)$ and apply regression in-context without retraining. Through large-scale OoD experiments across 33 diverse datasets and covariate integration studies, TabPFN-TS generally achieves the best accuracy and calibrated uncertainty, with MoTM offering a faster, robust alternative. The findings demonstrate the strong generalization and practical potential of time-indexed foundation models for real-world imputation tasks, while also highlighting trade-offs in computation and the benefits of incorporating covariates at inference. The work suggests a path toward off-the-shelf, zero-shot imputation across domains and points to future hybrid approaches that merge the strengths of both models and reduce inference costs.
Abstract
Foundation models for time series imputation remain largely unexplored. Recently, two such models, TabPFN-TS and MoTM, have emerged. These models share a common philosophy that places them within the family of time-indexed foundation models. This paper presents the first large-scale empirical study of these models for zero-shot imputation, which enables missing value recovery without retraining across a wide range of scenarios. We conduct extensive univariate experiments across 33 out-of-domain datasets (approximately 1.3M imputation windows) and evaluate their ability to integrate covariates at inference time to improve accuracy without fine-tuning. Our results demonstrate that time-indexed foundation models are a powerful and practical step toward achieving general-purpose, zero-shot imputation for real-world time series.