Open Access
2014 Model verification for Lévy-driven Ornstein-Uhlenbeck processes
Ibrahim Abdelrazeq, B. Gail Ivanoff, Rafał Kulik
Electron. J. Statist. 8(1): 1029-1062 (2014). DOI: 10.1214/14-EJS919


Lévy-Driven Ornstein-Uhlenbeck (or CAR(1)) processes were introduced by Barndorff-Nielsen and Shephard [1] as a model for stochastic volatility. Pham [17] developed a general formula to recover the unobserved driving process from the continuously observed CAR(1) process. When the CAR(1) process is observed at discrete times $0$, $h$, $2h$, $...$ $[T/h]h$ the driving process must be approximated. Approximated increments of the driving process are used to test the assumption that the CAR(1) process is Lévy-driven. Asymptotic behavior of the test statistic is investigated. Performance of the test is illustrated through simulation.


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Ibrahim Abdelrazeq. B. Gail Ivanoff. Rafał Kulik. "Model verification for Lévy-driven Ornstein-Uhlenbeck processes." Electron. J. Statist. 8 (1) 1029 - 1062, 2014.


Published: 2014
First available in Project Euclid: 31 July 2014

zbMATH: 1309.62146
MathSciNet: MR3263111
Digital Object Identifier: 10.1214/14-EJS919

Keywords: Lévy process , model verification , Ornstein-Uhlenbeck process , sample correlation , sampled process , test statistics

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.8 • No. 1 • 2014
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