Data Analysis Using a Coupled System of Ornstein–Uhlenbeck Equations Driven by Lévy Processes

Abstract

In this work, we have analyzed data sets from various fields using a coupled Ornstein–Uhlenbeck (OU) system of equations driven by Lévy processes. The Ornstein–Uhlenbeck model is well known for its ability to capture stochastic behaviors when used as a predictive model. There’s empirical evidence showing that there exist dependencies or correlations between events; thus, we may be able to model them together. Here we show such correlation between data from finance, geophysics and health as well as show the predictive performance when they are modeled with a coupled Ornstein–Uhlenbeck system of equations. The results show that the solution to the stochastic system provides a good fit to the data sets analyzed. In addition by comparing the results obtained when the BDLP is a Γ(a,b) process or an IG(a,b) process, we are able to deduce the best choice out of the two to model our data sets.

Keywords

• Ornstein–Uhlenbeck equation
• background driving Lévy process
• gamma process
• inverse Gaussian process
• coupled system
• sample paths