Time-Aware Prior Fitted Networks for Zero-Shot Forecasting with Exogenous Variables

arXiv cs.LG / 3/18/2026

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Key Points

ApolloPFN is introduced as a time-aware prior-data fitted network that explicitly incorporates exogenous covariates for zero-shot time-series forecasting.
It adds a synthetic data generation procedure to adapt tabular PFNs to time-series tasks, addressing failure modes when applying non-temporal PFNs to temporal data.
It includes time-aware architectural modifications that embed inductive biases to exploit time-series context, improving handling of spikes, regime changes, and discontinuities.
Empirical results show state-of-the-art performance on benchmarks like M5 and electric price forecasting, outperforming prior time-series foundation models such as Chronos, Sundial, TimesFM, TimeMoE, TimeLLM, and LagLlama.

Abstract

In many time series forecasting settings, the target time series is accompanied by exogenous covariates, such as promotions and prices in retail demand; temperature in energy load; calendar and holiday indicators for traffic or sales; and grid load or fuel costs in electricity pricing. Ignoring these exogenous signals can substantially degrade forecasting accuracy, particularly when they drive spikes, discontinuities, or regime and phase changes in the target series. Most current time series foundation models (e.g., Chronos, Sundial, TimesFM, TimeMoE, TimeLLM, and LagLlama) ignore exogenous covariates and make forecasts solely from the numerical time series history, thereby limiting their performance. In this paper, we develop ApolloPFN, a prior-data fitted network (PFN) that is time-aware (unlike prior PFNs) and that natively incorporates exogenous covariates (unlike prior univariate forecasters). Our design introduces two major advances: (i) a synthetic data generation procedure tailored to resolve the failure modes that arise when tabular (non-temporal) PFNs are applied to time series; and (ii) time-aware architectural modifications that embed inductive biases needed to exploit the time series context. We demonstrate that ApolloPFN achieves state-of-the-art results across benchmarks, such as M5 and electric price forecasting, that contain exogenous information.