Recent history functional linear models

We propose a variant of historical functional linear models for cases where the current response is affected by the predictor process in a window into the past. Different from the rectangular support of functional linear models, the triangular support of the historical functional linear models and the point-wise support of varying coefficient models, the current model has a sliding window support into the past. This idea leads to models that bridge the gap between varying coefficient models and functional linear (historic) models. By utilizing one-dimensional basis expansions and one-dimensional smoothing procedures, the proposed estimation algorithm is shown to have better performance and to be faster than the estimation procedures proposed for historical functional linear models.