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

• URL: http://arxiv.org/abs/2608.06748v1
• Date: Fri, 07 Aug 2026 03:16:25 GMT
• Title: KReF: Training-Free Retrieval for Long-Term Time-Series Forecasting and Predictive Uncertainty
• Abstract summary: We propose a training-free retrieval framework that treats retrieved historical futures as a querylocal empirical predictive distribution.<n>KReF embeds each lookback using statistics or frozen random Fourier features and retrieves similar historical lookback-future pairs.<n>Their similarity weights directly define predictive masses, quantiles, CRPS, and a weighted-mean point forecast.
• Score: 8.44268644654703
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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