Derivation of a State-Space Model by Functional Data Analysis

By approximating a stochastic process by means of spline interpolation of its sample-paths, a time dependent state-space model is introduced. Then we derive the expression of the associated transition matrix that allows to obtain a discrete model useful in applications. In order to essay the behaviour of the proposed models simulations on a narrow-band process are developed. Finally, the paper includes an application with real data obtained from the Stock Market of Madrid. Copyright Physica-Verlag 2003