Resumen de Multidimensional diagonalization of FAR(n) models for functional extrapolation

Román Salmerón Gómez , María Dolores Ruiz Medina

• The functional autoregressive model of order n (FAR(n)) extends to the infinite-dimensional space context the classical autoregressive model AR(n) (see, for example, Mourid, 1993). Such a model provides a suitable framework for the statistical analysis of functional data in several applied fields. In this paper, we derive a multidimensional diagonalization of the functional parameters (operators) involved in its formulation. The state equation is then transformed into an infinite-dimensional system of scalar state equations. Truncation, according to the operator norm associated with functional parameters, leads to a finitedimensional scalar version.We apply these results for implementation of Kalman filtering algorithm for functional extrapolation in FAR(n) models.