Una Aplicación de las Series de Tiempo Visto desde los Espacios De Hilbert

Abstract

In the present work a model will be chosen to estimate parameters and to use the model to improve and understand the operation generated by the series, as seen from the Hilbert L2 (Ω, F, P) spaces. Initially it will be shown that the space of all random variables X defined in Ω are a vector space and with a defined internal product will be a Hilbert space, supported by the theory of measurement and functional analysis, we introduce the relationship between stochastic spaces And the time series finding that the mathematical model for a time series is the concept of stochastic process, the properties of the autoregressive model will be stated and demonstrated. Finally, the above-mentioned theory will be applied to a particular example of the autoregressive model.