论文标题
二维功能时间序列的共形预测带
Conformal Prediction Bands for Two-Dimensional Functional Time Series
论文作者
论文摘要
时间不断发展的表面可以建模为二维功能时间序列，从而利用功能数据分析工具。为了利用这种方法，开发了对此类复杂数据的预测框架。主要重点围绕共形预测，这是一种多功能的非参数范式，用于量化预测问题的不确定性。基于功能时间序列的保形预测的最新变化，提出了二维功能时间序列的概率预测方案，同时提供了订单One的功能自动回归过程的扩展到此设置。引入了后一个过程的估计技术，并根据由此产生的预测区域比较其性能。最后，提出的预测程序和不确定性量化技术应用于真实数据集，收集了黑海海平面异常的每日观察
Time evolving surfaces can be modeled as two-dimensional Functional time series, exploiting the tools of Functional data analysis. Leveraging this approach, a forecasting framework for such complex data is developed. The main focus revolves around Conformal Prediction, a versatile nonparametric paradigm used to quantify uncertainty in prediction problems. Building upon recent variations of Conformal Prediction for Functional time series, a probabilistic forecasting scheme for two-dimensional functional time series is presented, while providing an extension of Functional Autoregressive Processes of order one to this setting. Estimation techniques for the latter process are introduced and their performance are compared in terms of the resulting prediction regions. Finally, the proposed forecasting procedure and the uncertainty quantification technique are applied to a real dataset, collecting daily observations of Sea Level Anomalies of the Black Sea
