KReF: Training-Free Retrieval for Long-Term Time-Series Forecasting and Predictive Uncertainty
Summary
KReF introduces a training-free retrieval framework for long-term time-series forecasting that constructs empirical predictive distributions from similar historical lookback-future pairs, achieving strong CRPS performance across multiple benchmarks.
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# KReF: Training-Free Retrieval for Long-Term Time-Series Forecasting and Predictive Uncertainty Source: [https://arxiv.org/abs/2608.06748](https://arxiv.org/abs/2608.06748) [View PDF](https://arxiv.org/pdf/2608.06748) > 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\. ## Submission history From: Yang Zhang \[[view email](https://arxiv.org/show-email/c16b3fe2/2608.06748)\] **\[v1\]**Fri, 7 Aug 2026 03:16:25 UTC \(1,554 KB\)
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