Ornstein-Uhlenbeck type processes with heavy tails
We consider a transformed Ornstein--Uhlenbeck process model that can be a good candidate for modeling real-life processes characterized by a combination of time-reverting behavior with heavy distribution tails. We begin with presenting the results of an exploratory statistical analysis of the log prices of a major Australian public company, demonstrating several key features typical of such time series. Motivated by these findings, we suggest a simple transformed Ornstein--Uhlenbeck process model and analyze its properties showing that the model is capable of replicating our empirical findings. We also discuss three different estimators for the drift coefficient in the underlying (unobservable) Ornstein--Uhlenbeck process which is the key descriptor of dependence in the process.