Prediction Bands for Functional Data Based on Depth Measures

Abstract

We propose a new methodology for predicting a partially observed curve from a functional data sample. The novelty of our approach relies on the selection of sample curves which form tight bands that preserve the shape of the curve to predict, making this a deep datum. The involved subsampling problem is dealt by algorithms specially designed to be used in conjunction with two different tools for computing central regions for functional data. From this merge, we obtain prediction bands for the unobserved part of the curve in question. We test our algorithms by forecasting the Spanish electricity demand and imputing missing daily temperatures. The results are consistent with our simulation that show that we can predict at the far horizon.