PaP-NF: Probabilistic Long-Term Time Series Forecasting via Prefix-as-Prompt Reprogramming and Normalizing Flows

• URL: http://arxiv.org/abs/2605.23219v1
• Date: Fri, 22 May 2026 04:22:14 GMT
• Title: PaP-NF: Probabilistic Long-Term Time Series Forecasting via Prefix-as-Prompt Reprogramming and Normalizing Flows
• Abstract summary: Time series forecasting plays a central role in many real-world applications.<n>Most existing approaches rely on deterministic models, making single-point predictions insufficient.<n>We propose PaP-NF, a probabilistic forecasting framework that aligns continuous time series representations with a frozen large language model.
• Score: 7.968962975207229
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Time series forecasting plays a central role in many real-world applications and has been extensively studied. Most existing approaches rely on deterministic models. However, real-world environments exhibit inherently uncertain and complex future behaviors, making single-point predictions insufficient. This highlights the need for probabilistic forecasting methods that can quantify and represent uncertainty. In this work, we propose PaP-NF, a probabilistic forecasting framework that aligns continuous time series representations with a frozen large language model (LLM) using a Prefix-as-Prompt mechanism, and conditions a normalizing flow decoder on the global context extracted by the LLM. The quality of the resulting predictive distributions is evaluated using the Continuous Ranked Probability Score (CRPS), a standard metric in probabilistic forecasting. Across a variety of long-term forecasting benchmarks, PaP-NF robustly captures multi-modal uncertainty while maintaining competitive point forecasting accuracy. The official implementation is available at: https://github.com/democracy04/PaP-NF

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