Pronóstico en Series de Tiempo de Media Móvil Finitas Sustentado desde los Espacios de Hilbert

Abstract

The purpose of this work is to show the mathematical basis for predictions to stationary series, more specifically those series that have a behavior MA (q) called movil average processes of order q these series have some special characteristics in their mean, variance, Self-covariance function, simple and partial autocorrelation functions, as well as the appearance of their correlograms. In order to do this, we are working with space-oriented concepts of measurement theory L2 (Ω, F, P), a space with a inner product which fulfills all the necessary characteristics to be a Hilbert space. Finally a small simulation is performed in R with which it is tried to contrast all the theory worked with a set of data.