Smoothing splines for trend estimation and prediction in time series

We consider the use of generalized additive models with correlated errors for analysing trends in time series. The trend is represented as a smoothing spline so that it can be extrapolated. A method is proposed for choosing the smoothing parameter. It is based on the ability to predict a short term into the future. The choice not only addresses the purpose in hand, but also performs very well, and avoids the tendency to under‐smooth or to interpolate the data that can occur with other data‐driven methods used to choose the smoothing parameter. The method is applied to data from a chemical process and to stream salinity measurements.