Ornstein--Uhlenbeck Type Processes with Heavy Distribution 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 pr...

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Bibliographic Details
Published in:Theory of probability and its applications 2013-01, Vol.57 (3), p.396-418
Main Authors: Borovkov, K, Decrouez, G
Format: Article
Language:English
Subjects:
Applied mathematics
Australia
Data analysis
Drift
Empirical analysis
Estimators
Mathematical models
Replicating
Securities prices
Statistical analysis
Stock prices
Time series
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Summary: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. [PUBLICATION ABSTRACT]
ISSN:0040-585X
1095-7219
DOI:10.1137/S0040585X97986102