B1094
Title: Simultaneous predictive bands for functional time series using minimum entropy sets
Authors: Jairo Cugliari - Université Lumière Lyon 2 (France) [presenting]
Nicolas Hernandez - University of Cambridge (United Kingdom)
Julien Jacques - University Lyon II (France)
Abstract: Functional Time Series (FTS) are sequences of dependent random elements taking values on some functional space. Most of the research on this domain is focused on producing a predictor able to forecast the value of the next function having observed a part of the sequence. For this, the Autoregressive Hilbertian process is a suitable framework. We address the problem of constructing simultaneous predictive confidence bands for a stationary FTS. The method is based on an entropy measure for stochastic processes, in particular FTS. To construct predictive bands, we use a functional bootstrap procedure that allows us to estimate the prediction law through the use of pseudo-predictions. Each pseudo-realisation is then projected into a finite-dimensional space associated with a functional basis. We use Reproducing Kernel Hilbert Spaces (RKHS) to represent the functions, considering then the basis associated with the reproducing kernel. Using a simple decision rule, we classify the points on the projected space among those belonging to the minimum entropy set and those that do not. We push back the minimum entropy set to the functional space and construct a band using the regularity property of the RKHS. The proposed methodology is illustrated through artificial and real-world data sets.