The Functional Data Analysis (FDA) approach is proposed towards modelling time series data because of recognition of the need to better analyse, model and forecast data observed over time. This approach allows for smooth functions of age, is robust for outlying years due to wars and epidemics, and provides a modelling framework that is easily adapted to allow for constraints and other information. Ideas from functional data analysis, nonparametric smoothing and robust statistics are combined to form a methodology that is widely applicable to any functional time series data observed discretely and possibly with error. The model is a generalization of the Lee–Carter (LC) model and is applied to French mortality data, Australian fertility data and Finish injury data, and the forecasts obtained are shown to be superior to those from the LC method and several of its variants. A new approach called Forecast REsidual Sum of Squares (FRESS) is also proposed to check the forecast accuracy. Using the specific example of Finish injury data, FRESS demonstrated that FDA is superior over the more commonly reported ordinary least square, Poisson and negative binomial modelling approaches in terms of forecast accuracy.