Variable selection for the prediction of C[0,1]-valued AR processes using RKHS

A model for the prediction of functional time series is introduced, where observations are assumed to be realizations of a C[0,1]-valued process. We model the dependence of the data with a non-standard autoregressive structure, motivated in terms of the Reproducing Kernel Hilbert Space (RKHS) generated by the covariance kernel of the data. The general definition has as particular case a set of finite-dimensional models based on marginal variables of the process. Thus, this approach is especially useful to find relevant points for prediction (sometimes called "impact points"). Some examples show that this model has a good amount of generality. In addition, problems like the non-invertibility of the covariance operators in function spaces can be circumvented using this methodology. A simulation study and two real data examples are presented to evaluate the performance of the proposed predictors.      «

A model for the prediction of functional time series is introduced, where observations are assumed to be realizations of a C[0,1]-valued process. We model the dependence of the data with a non-standard autoregressive structure, motivated in terms of the Reproducing Kernel Hilbert Space (RKHS) generated by the covariance kernel of the data. The general definition has as particular case a set of finite-dimensional models based on marginal variables of the process. Thus, this approach is especially...     »