El Departamento de Matemáticas y Estadística de la Universidad Torcuato Di Tella invita al seminario sobre Minimum entropy predictive bands for functional time series forecasting, a cargo de Nicolás Hernández (Dr. en Estadística por la Universidad Carlos III de Madrid).

Abstract
Functional Time Series (FTS) are sequences of dependent random elements taking values on some functional space. Most of the research on this domain focuses on producing a predictor able to forecast the next function, having observed a part of the sequence. For this, the Autoregressive Hilbertian process is a suitable framework. Here, 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. To construct predictive bands, we use a Reproducing Kernel Hilbert Spaces (RKHS) to represent the functions and a functional bootstrap procedure that allows us to estimate the prediction law and a Reproducing Kernel Hilbert Spaces (RKHS) to represent the functions, considering then the basis associated to the reproducing kernel. We then classify the points on the projected space according to those that belong to the minimum entropy set (MES) and those that do not. We map the minimum entropy set back to the functional space and construct a band using the regularity property of the RKHS. The proposed methodology is illustrated through artificial and real data sets.

El seminario se dará en español.

Nicolás Hernández. IMSS Senior Research Fellow at the Department of Statistical Science at University College London. He recently moved to UCL to develop his own research project about: ‘‘Inference for High-Dimensional and Functional Data’’. Previously, Nicolás was a Postdoctoral Research Associate at the MRC Biostatistics Unit of the University of Cambridge. Nicolás holds a PhD in Statistics from the Department of Statistics at Universidad Carlos III de Madrid.