Computational Statistics (2003) 18:533-546 © Physica-Verlag 2003 Derivation of a State-Space Model by Functional Data Analysis Mariano J. Valderrama!, Monica Ortega-Moreno 2 , Pedro Gonzalez 3 and Ana M. Aguilera 4 Department of Statistics and Operations Research, Faculty of Pharmacy, University of-Granada. 18071 Granada, Spain. E-mail: valderra@ugr.es 2 Department of General Economics and Statistics, Faculty of Economics Sciences, University of Huelva. 21071 Huelva, Spain. E-mail: orteg- amo@uhu.es 3 Department of Applied Mathematics, School of Civil Engineering, University of Granada. 18071 Granada, Spain. E-mail: prodelas@ugr.es 4 Department of Statistics and Operations Research, Faculty of Sciences, University of Granada. 18071 Granada, Spain. E-mail: aaguiler@ugr.es Summary 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. Keywords: Functional PCA; B-spline; state-space model; Kalman filter; narrow-band process.