We propose an approximate factor model for time-dependent curve data that represents a functional time series as the aggregate of a predictive low-dimensional component and an unpredictive infinite-dimensional component. Suitable identification conditions lead to a two-stage estimation procedure based on functional principal components, and the number of factors is estimated consistently through an information criterion-based approach. The methodology is applied to the problem of modeling and predicting yield curves. Our results indicate that more than three factors are required to characterize the dynamics of the term structure of bond yields.

翻译：我们为基于时间的曲线数据提出了一个近似系数模型,该模型代表一个功能时间序列,作为预测的低维组成部分和不预知的无限维组成部分的总和。适当的识别条件导致基于功能性主要组成部分的两阶段估算程序,并且以基于信息的标准方法对系数的数量进行一致估计。该方法适用于计算和预测收益率曲线的问题。我们的结果表明,需要三个以上因素来说明债券收益率术语结构的动态。