时间序列的有效且高效的分割保形回归

中文摘要 AI 辅助

我们研究了保形分位数回归和保形中位数回归，这些方法在时间序列的一个区块上拟合模型，并在相邻区块上校准保形区间。现有的时间序列保形预测理论主要依赖于混合条件，这些条件难以从时间序列模型中验证，并且对于许多标准过程（包括具有短记忆的简单过程）会失效。我们用函数依赖度量取代了这一理论工具箱，该度量原则上能适应长记忆观测。时间序列保形区间长度的准确性研究不足。据我们所知，本文是首个同时为时间序列上的分割保形回归建立非渐近覆盖保证和区间长度准确性的工作。此外，对于具有长记忆的高斯线性过程，其中中心的估计及其校准均收敛缓慢，我们为长度误差建立了更精确的速率。我们表明，校准后的长度比估计的中心本身收敛得更快，并且当校准区块相对于训练区块足够大时，我们为通常的中心提供了匹配的下界。据我们所知，这是首次专门针对长记忆的保形区间长度的理论分析。

英文摘要

We study conformalized quantile regression and conformalized median regression that fit a model on one block of a time series and calibrate the conformal interval on the adjacent block. The existing theory of conformal prediction for time series rests largely on mixing conditions, which are hard to verify from a time-series model and fail for many standard processes, including simple ones with short memory. We replace this theoretical toolbox with the functional dependence measure, which in principle accommodates long-memory observations. The accuracy of the conformal interval length for time series has been understudied. To the best of our knowledge, this paper is the first work that establishes non-asymptotic coverage guarantees and accuracy of interval length simultaneously for split conformal regression on time series. Furthermore, for Gaussian linear processes with long memory, where both the estimation of the center and its calibration converge slowly, we establish a sharper rate for the length error. We show that the calibrated length converges faster than the estimated center itself, and provide a matching lower bound for the usual centers when the calibration block is sufficiently large relative to the training block. To our knowledge, this is the first theoretical analysis of conformal interval length dedicated to long memory.

发表机构

• University of Chicago（芝加哥大学）
• Illinois Institute of Technology（伊利诺伊理工学院）

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