Modeling stationary data by a class of generalized Ornstein-Uhlenbeck processes: The Gaussian case

© 2014 Springer International Publishing Switzerland. The Ornstein-Uhlenbeck (OU) process is a well known continuous– time interpolation of the discrete–time autoregressive process of order one, the AR(1). We propose a generalization of the OU process that resembles the construction of autoregressive processes of higher order p > 1 from the AR(1). The higher order OU processes thus obtained are called Ornstein-Uhlenbeck processes of order p (denoted OU(p)), and constitute a family of parsimonious models able to adjust slowly decaying covariances. We show that the OU(p) processes are contained in the family of autoregressive moving averages of order (p, p − 1), the ARMA (p, p−1), and that their parameters and covariances can be computed efficiently. Experiments on real data show that the empirical autocorrelation for large lags can be well modeled with OU(p) processes with approximately half the number of parameters than ARMA processes.