  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.
