Informatics and Applications
2016, Volume 10, Issue 4, pp 46-56
REGIME SWITCHING DETECTION FOR THE LEVY DRIVEN ORNSTEIN-UHLENBECK PROCESS USING CUSUM METHODS
- A. V. Chertok
- A. I. Kadaner
- G. T. Khazeeva
- I. A. Sokolov
Abstract
The article considers using a trending Ornstein-Uhlenbeck process, driven by a Levy process, for modeling financial time series. The authors demonstrate that the Levy driven model gives more flexibility to describe financial time series than the simple classical model. In particular, the Levy driven model allows modeling distributions with heavy tails, which is a common property of time series in real applications. The authors describe efficient methods for estimating model parameters using such methods as OLS (ordinary least squares) and RLS (regularized least squares). The article also solves the regime switching problem in a real time data stream. The authors built an algorithm based on CUSUM (CUmulative SUM) methods that is capable of determining regime switches consecutively as they happen online and keep model parameters up to date. Solution of the regime switching problem is important in real applications, since the dynamics of real systems tend to change over time under the influence of external factors.
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[+] About this article
Title
REGIME SWITCHING DETECTION FOR THE LEVY DRIVEN ORNSTEIN-UHLENBECK PROCESS USING CUSUM METHODS
Journal
Informatics and Applications
2016, Volume 10, Issue 4, pp 46-56
Cover Date
2016-12-30
DOI
10.14357/19922264160405
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
random process; mean-reverting process; Ornstein-Uhlenbeck process driven by Levy process; trending Ornstein-Uhlenbeck process; regime switch; change point detection; CUSUM algorithm
Authors
A. V. Chertok  ,  ,
A. I. Kadaner ,  ,
G. T. Khazeeva , and I. A. Sokolov 
Author Affiliations
Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation
Sberbank of Russia, 19 Vavilov Str., Moscow 117999, Russian Federation
Faculty of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, Main Building, Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation
Institute of Informatics Problems, Federal Research Center “Computer Sciences and Control” of the Russian
Academy of Sciences, 44-2 Vavilov Str.,Moscow 119333, Russian Federation
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