KReF: Training-Free Retrieval for Long-Term Time-Series Forecasting and Predictive Uncertainty
This paper introduces a novel training-free approach for probabilistic long-term forecasting, offering a new inductive bias that could benefit practitioners in time-series domains.
KReF is a training-free retrieval framework for probabilistic long-term time-series forecasting that treats retrieved historical futures as an empirical predictive distribution. It achieves the lowest CRPS in all 12 dataset-embedding settings and the lowest IS90 in 9 settings across six benchmarks and four horizons, while matching or surpassing trained baselines on two datasets for point forecasts.
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.