Fractional iterated Ornstein-Uhlenbeck Processes

Abstract: In this work we present a Gaussian process that arise from the iteration of p fractional Ornstein-Uhlenbeck processes generated by the same fractional Brownian motion. This iteration results, when the values of lambdas are pairwise differents, in a particular linear combination of those processes. Although for $H>1/2$ each term of the linear combination is a long memory processes, we prove that it results in a short memory processes. We include applications to real data that show improvement in predictive performance compared with different ARMA models.