We propose a novel approximate factor model tailored for analyzing time-dependent curve data. Our model decomposes such data into two distinct components: a low-dimensional predictable factor component and an unpredictable error term. These components are identified through the autocovariance structure of the underlying functional time series. The model parameters are consistently estimated using the eigencomponents of a cumulative autocovariance operator and an information criterion is proposed to determine the appropriate number of factors. The methodology is applied to yield curve modeling and forecasting. Our results indicate that more than three factors are required to characterize the dynamics of the term structure of bond yields.

翻译：本文提出一种新颖的近似因子模型，专门用于分析时间相关的曲线数据。该模型将此类数据分解为两个独立分量：一个低维可预测因子分量和一个不可预测的误差项。这些分量通过基础函数时间序列的自协方差结构进行识别。模型参数通过累积自协方差算子的特征分量得到一致估计，并提出一种信息准则来确定适当的因子数量。该方法应用于收益率曲线建模与预测。研究结果表明，需要三个以上因子才能刻画债券收益率期限结构的动态特征。