High-dimensional functional time series forecasting

In this paper, we address the problem of forecasting high-dimensional functional time series through a two-fold dimension reduction procedure. Dynamic functional principal component analysis is applied to reduce each infinite-dimension functional time series to a vector. We use factor model as a further dimension reduction technique so that only a small number of latent factors are preserved. Simple time series models can be used to forecast the factors and forecast of the functions can be constructed. The proposed method is easy to implement especially when the dimension of functional time series is large. We show the superiority of our approach by both simulation studies and an application to Japan mortality rates data.