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Title: Minimum entropy forecast for functional time series Authors:  Nicolas Hernandez - Universidad Carlos III de Madrid (Spain) [presenting]
Alberto Munoz - Departmento de Estadistica - Universidad Carlos III de Madrid (Spain)
Gabriel Martos - Fundacion Universidad Torcuato Di Tella (Argentina)
Abstract: Consider a functional time series (FTS) data set $\{X_k\}_{k \in \{1,\cdots,n\}}$, where each $X_k$ is a random function $X_k(t)$, $t \in [a,b]$. We introduce a novel approach to forecast functional time series, based on the truncated multivariate representation of the time series, obtained by projecting them onto an appropriate Reproducing Kernel Hilbert Space (RKHS). We propose a modelization scheme to obtain the $h$ steps ahead prediction, $X_{(k+1)}(t),\cdots,X_{(k+h)}(t)$, from the multivariate RKHS representation of the FTS data set. A bootstrap method for dependent data and a minimum entropy criterion is then applied to obtain the point forecast and the confidence bands. As an interesting application, we conduct an analysis of fertility and mortality rate curves of functional time series forecast.