Using observed functional data to simulate a stochastic process via a random multiplicative cascade model

Abstract

Considering functional data and an associated binary response, a method based on the definition of special Random Multiplicative Cascades to simulate the underlying stochastic process is proposed. It will be considered a class S of stochastic processes whose realizations are real continuous piecewise linear functions with a constrain on the increment and the family R of all binary responses Y associated to a process X in S. Considering data from a continuous phenomenon evolving in a time interval [0, T] which can be simulated by a pair (X, Y ) 2 S × R, a prediction tool which would make it possible to predict Y at each point of [0, T] is introduced. An application to data from an industrial kneading process is considered. © Springer-Verlag Berlin Heidelberg 2010.