  A characteristic feature of functional data is the presence of phase
variability in addition to amplitude variability. Existing functional
regression methods do not handle time variability in an explicit and efficient
way. In this paper we introduce a functional regression method that
incorporates time warping as an intrinsic part of the model. The method
achieves good predictive power in a parsimonious way and allows unified
statistical inference about phase and amplitude components. The asymptotic
distribution of the estimators is derived and the finite-sample properties are
studied by simulation. An example of application involving ground-level ozone
trajectories is presented.
