标题： 部分观测未来曲线的功能时间序列预测 显示英文标题

标题： Functional time series prediction under partial observation of the future curve

摘要： 本文解决的是函数时间序列分析中最基本的目标之一，即为未来的函数提供可靠预测。 现有的预测完整未来函数观测值的方法仅使用完全观测的轨迹。 我们开发了一种新方法，称为部分函数预测（PFP），该方法同时使用完全观测的轨迹和待预测轨迹的部分信息（可用的部分数据）。 PFP 方法基于最小化预测误差自动选择调参准则，并建立了 PFP 预测的收敛速率。 模拟研究显示，在均方预测误差方面，将部分观测轨迹纳入预测优于现有方法。 PFP 方法在环境数据和交通流量数据的分析中被证明更优。 显示英文摘要

摘要： This paper tackles one of the most fundamental goals in functional time series analysis which is to provide reliable predictions for future functions. Existing methods for predicting a complete future functional observation use only completely observed trajectories. We develop a new method, called partial functional prediction (PFP), which uses both completely observed trajectories and partial information (available partial data) on the trajectory to be predicted. The PFP method includes an automatic selection criterion for tuning parameters based on minimizing the prediction error, and the convergence rate of the PFP prediction is established. Simulation studies demonstrate that incorporating partially observed trajectory in the prediction outperforms existing methods with respect to mean squared prediction error. The PFP method is illustrated to be superior in the analysis of environmental data and traffic flow data.