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

TL;DR

This paper introduces a novel RKHS-based autoregressive model for functional time series prediction, enabling effective variable selection and dimension reduction with interpretable results, demonstrated through real and simulated data.

Contribution

It proposes a new RKHS-driven autoregressive framework for functional data, improving variable selection and interpretability in functional time series prediction.

Findings

Competitive prediction accuracy on real and simulated data

Effective identification of relevant points on curves

Enhanced interpretability of model results

Abstract

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.