标题： 在部分观测未来曲线情况下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： 本文解决的是功能时间序列分析中最基本的目标之一，即为函数提供可靠预测。现有的功能时间序列方法旨在根据一组观察到的完整轨迹来预测一个完整的未来功能观测值。本文讨论的问题是，如何将预测方法推广到部分信息可用于下一个轨迹的情况下，以提高预测准确性。为了解决这个问题，我们提出了一种新方法“部分功能预测（PFP）”。所提出的方法结合了“下一区间”预测和完全功能回归预测，从而使轨迹的部分观测部分有助于生成未来曲线未观测部分的更好预测。在PFP中，我们包括基于最小化预测误差的调参自动选择准则。模拟结果表明，所提出的方法在均方预测误差方面可以优于现有方法，其实际效用在环境和交通流量数据的分析中得到了说明。 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 functions. Existing functional time series methods seek to predict a complete future functional observation based on a set of observed complete trajectories. The problem of interest discussed here is how to advance prediction methodology to cases where partial information on the next trajectory is available, with the aim of improving prediction accuracy. To solve this problem, we propose a new method "partial functional prediction (PFP)". The proposed method combines "next-interval" prediction and fully functional regression prediction, so that the partially observed part of the trajectory can aid in producing a better prediction for the unobserved part of the future curve. In PFP, we include automatic selection criterion for tuning parameters based on minimizing the prediction error. Simulations indicate that the proposed method can outperform existing methods with respect to mean-square prediction error and its practical utility is illustrated in an analysis of environmental and traffic flow data.