Method of Moments Estimation of Ornstein-Uhlenbeck Processes Driven by General Lévy Process

Details Method of Moments Estimation of Ornstein-Uhlenbeck Processes Driven by General Lévy Process Method of Moments Estimation of Ornstein-Uhlenbeck Processes Driven by General Lévy Process

2008-07-17

arxiv.org/abs/0807.2832v4

ANNALES de l'I.S.U.P. Vol 53 - Fascicule 2-3, 2009, pp. 3-19

Mathematics

Probability

15 pages, 4 Postscript figures; corrected minor typos, final published version

Scientific paper

Ornstein-Uhlenbeck processes driven by general L\'{e}vy process are considered in this paper. We derive strongly consistent estimators for the moments of the underlying L\'{e}vy process and for the mean reverting parameter of the Ornstein-Uhlenbeck process. Moreover, we prove that the estimators are asymptotically normal. Finally, we test the empirical performance of our estimators in a simulation study and we fit the model to real data.

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