Forecasting functional time series

We propose forecasting functional time series using weighted functional principal component regression and weighted functional partial least squares regression. These approaches allow for smooth functions, assign higher weights to more recent data, and provide a modeling scheme that is easily adapted to allow for constraints and other information. We illustrate our approaches using age-specific French female mortality rates from 1816 to 2006 and age-specific Australian fertility rates from 1921 to 2006, and show that these weighted methods improve forecast accuracy in comparison to their unweighted counterparts. We also propose two new bootstrap methods to construct prediction intervals, and evaluate and compare their empirical coverage probabilities.