Accurate curve forecasting is of vital importance for policy planning, decision making and resource allocation in many engineering and industrial applications. In this paper we establish a theoretical foundation for the optimal short-term linear prediction of non-stationary functional or curve time series with smoothly time-varying data generating mechanisms. The core of this work is to establish a unified functional auto-regressive approximation result for a general class of locally stationary functional time series. A double sieve expansion method is proposed and theoretically verified for the asymptotic optimal forecasting. A telecommunication traffic data set is used to illustrate the usefulness of the proposed theory and methodology.

翻译：精确的曲线预测对于许多工程和工业应用中的政策规划、决策制定及资源分配至关重要。本文为数据生成机制随时间平滑变化的非平稳函数型（或曲线）时间序列的最优短期线性预测建立了理论基础。本研究的核心是为一般类别的局部平稳函数型时间序列建立统一的函数型自回归逼近结果。我们提出了一种双重筛展开方法，并从理论上验证了其在渐近最优预测中的有效性。最后，通过一个电信流量数据集展示了所提理论与方法的实用价值。