Ornstein-Uhlenbeck type processes with heavy distribution tails

TL;DR

This paper introduces a transformed Ornstein-Uhlenbeck process model tailored for real-world data exhibiting mean-reversion and heavy tails, supported by empirical analysis of Australian stock prices.

Contribution

It proposes a novel transformed Ornstein-Uhlenbeck model capable of capturing heavy tails and time-reversion, with analysis of estimators for the drift coefficient.

Findings

Model replicates empirical heavy-tailed features

Analysis of three estimators for the drift coefficient

Empirical validation with Australian stock data

Abstract

We consider a transformed Ornstein-Uhlenbeck process model that can be a good candidate for modelling real-life processes characterized by a combination of time-reverting behaviour 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.