A 3-component superposed Ornstein-Uhlenbeck model applied to financial stock markets

Understanding stock behaviors not only benefits retail or corporate investors but also helps governments in tracking the economic growth of their countries. This speaks to the many existing and ongoing research on financial indices. One such interesting area of research has been to model financial stocks using the Ornstein-Uhlenbeck model (OU model). Research methods that use the OU model to forecast financial stocks have shown that in most cases, such data deviate from normal behavior and are best modeled with non-Gaussian processes (Habtemicael et al. (2014), Tweneboah (2020)). In this work, we develop a complete numerical approach to estimate the rate parameters and the weights for the Superposed OU-model. We also provide further experimentation on the improvement of the OU model as a result of the superposition. To do this, we simulate a 3-Component OU-model and compare its performance with the 2-Component OU model and the Ordinary OU model by means of their corresponding root mean squared errors. We also compare the performance of our model when the background driving Levy process is either a Gamma process or an Inverse Gaussian process.