Variable Selection for the Prediction of C[0,1]-Valued Autoregressive Processes using Reproducing Kernel Hilbert Spaces

A model for the prediction of functional time series is introduced, where observations are assumed to be continuous random functions. We model the dependence of the data with a nonstandard autoregressive structure, motivated in terms of the reproducing kernel Hilbert space (RKHS) generated by the auto-covariance function of the data. The new approach helps to find relevant points of the curves in terms of prediction accuracy. This dimension reduction technique is particularly useful for applications, since the results are usually directly interpretable in terms of the original curves. An empirical study involving real and simulated data is included, which generates competitive results. Supplementary material includes R-code, tables, and mathematical comments.