用自适应校准方法提升非平稳时间序列的预测置信区间可靠性。
Adaptive Regime-Switching Forecasts with Distribution-Free Uncertainty: Deep Switching State-Space Models Meet Conformal Prediction
- 结合深度切换状态空间模型与自适应分位数推断，实现无需分布假设的不确定性估计。
- 在真实和合成数据上，预测带覆盖率接近理论值且区间更紧凑。
- 适用于需要可靠置信区间的金融、气象等非平稳时序场景。
regime 转换常导致时间序列非平稳，使得不确定性校准与点预测精度同样重要。本文通过将深度切换状态空间模型（Deep Switching State Space Models）与自适应分位数推断（ACI）及其聚合版本（AgACI）相结合，研究了无分布假设下的回归切换预测。我们还提出一个统一的分位数封装器，可作用于 S4、MC-Dropout GRU、稀疏高斯过程及变化点局部模型等强基线模型，在非平稳性和模型误设条件下提供具有有限样本边缘保证的在线预测带。在合成与真实数据集上，校准后的预测器实现了接近名义覆盖率的性能，同时保持了良好的预测精度，并普遍提升了预测带效率。
原文摘要 · Abstract (English)
Regime transitions routinely break stationarity in time series, making calibrated uncertainty as important as point accuracy. We study distribution-free uncertainty for regime-switching forecasting by coupling Deep Switching State Space Models with Adaptive Conformal Inference (ACI) and its aggregated variant (AgACI). We also introduce a unified conformal wrapper that sits atop strong sequence baselines including S4, MC-Dropout GRU, sparse Gaussian processes, and a change-point local model to produce online predictive bands with finite-sample marginal guarantees under nonstationarity and model misspecification. Across synthetic and real datasets, conformalized forecasters achieve near-nominal coverage with competitive accuracy and generally improved band efficiency.
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