CoSPOT: LLM-Based Online Time Series Forecasting with Spectral Prompts

Online Time Series Forecasting (OTSF) requires models to adapt continuously to evolving data and non-stationary environments. Existing methods, often relying on memory buffer-based retrieval, struggle with long-term adaptation and generalizing to entirely new patterns. This paper introduces CoSPOT, a novel framework that leverages the powerful few-shot capabilities of pre-trained Large Language Models (LLMs) for OTSF. CoSPOT uses a frozen LLM as its core online forecaster, minimizing the number of parameters that need updating during the online phase. Its key innovation lies in "compositional spectral prompts." Instead of feeding raw time series data directly, CoSPOT decomposes the time series into frequency bases. It then composes corresponding spectral basis prompts according to their amplitudes. This frequency-domain representation allows the LLM to be guided by the overall distribution of the input, enabling it to generalize to unseen patterns by forming new combinations of learned basis prompts. Extensive experiments on real-world datasets demonstrate CoSPOT's superior performance and practicality in challenging online scenarios, including extended online phases and cross-dataset settings with significant distribution shifts.