KReF: Training-Free Retrieval for Long-Term Time-Series Forecasting and Predictive Uncertainty

2026-08-06

AI Summary

This work addresses key challenges in long-term time series forecasting—namely, high model dependency, difficulty in capturing the full predictive distribution, and delayed feedback—by proposing KReF, a training-free framework. KReF introduces retrieval as an inductive bias for the first time, leveraging either handcrafted statistical features or frozen random Fourier feature embeddings of the lookback window to retrieve historically similar segments and construct a local empirical distribution. Point forecasts, quantiles, and uncertainty intervals are then generated via similarity-weighted aggregation, with prediction intervals adaptively calibrated using probability integral transform. Evaluated across six benchmark datasets and four forecast horizons (12 settings total), KReF achieves the lowest Continuous Ranked Probability Score (CRPS) overall, obtains the best Interval Score at 90% coverage (IS90) in nine settings, and outperforms trainable baselines in point forecasting on two out of six datasets.

Abstract

Probabilistic long-term time-series forecasting commonly relies on trained models. Training-free conformal methods typically construct intervals around a pre-existing point forecaster and do not natively represent a complete predictive distribution; sequential variants additionally suffer from increasingly delayed feedback at long horizons. We propose KReF, a training-free retrieval framework that treats retrieved historical futures as a querylocal empirical predictive distribution. After robust preprocessing, KReF embeds each lookback using handcrafted statistics or frozen random Fourier features and retrieves similar historical lookback-future pairs. Their similarity weights directly define predictive masses, quantiles, CRPS, and a weighted-mean point forecast. KReF further uses the observed query lookback to construct a probability-integral-transform map and applies validation-selected expansion and shrinkage rates to adapt interval boundaries. Across six LTSF benchmarks and four horizons, KReF obtains the lowest CRPS in all 12 dataset-embedding settings and the lowest IS90 in 9 settings. Without gradient-based fitting, its point forecasts also match or surpass trained baselines on two of six datasets. An archive-oracle analysis further reveals substantial headroom under finer horizon- and channel-wise routing. These results establish retrieval as a useful and underexplored inductive bias for LTSF.

Problem

• long-term time-series forecasting
• predictive uncertainty
• training-free methods
• conformal prediction
• retrieval-based forecasting

Innovation

• training-free
• retrieval-based forecasting
• predictive uncertainty
• long-term time-series forecasting
• conformal prediction