  A novel method for noise reduction in the setting of curve time series with
error contamination is proposed, based on extending the framework of functional
principal component analysis (FPCA). We employ the underlying,
finite-dimensional dynamics of the functional time series to separate the
serially dependent dynamical part of the observed curves from the noise. Upon
identifying the subspaces of the signal and idiosyncratic components, we
construct a projection of the observed curve time series along the noise
subspace, resulting in an estimate of the underlying denoised curves. This
projection is optimal in the sense that it minimizes the mean integrated
squared error. By applying our method to similated and real data, we show the
denoising estimator is consistent and outperforms existing denoising
techniques. Furthermore, we show it can be used as a pre-processing step to
improve forecasting.
