Functional convolution models

This article considers the application of functional data analysis methods to modelling particulate matter emission profiles from dynamometer experiments. In particular the functional convolution model is introduced as an extension of the distributed lag model to functional (smooth and continuous) observations. We present a penalized ordinary least squares estimator for the model and a novel bootstrap procedure to provide pointwise confidence regions for the estimated convolution functions. The model is illustrated on the Coordinating Research Council E55/59 study of diesel truck emissions.