Abstract
This paper presents an empirical likelihood estimation procedure for parameters of the discretely sampled process of Ornstein-Uhlenbeck type. The proposed procedure is based on the conditional characteristic function, and the maximum empirical likelihood estimator is proved to be consistent and asymptotically normal. Moreover, this estimator is shown to be asymptotically efficient under some mild conditions. When the background driving Lévy process is of type A or B, we show that the intensity parameter can be exactly recovered, and we study the maximum empirical likelihood estimator with the plug-in estimated intensity parameter. Testing procedures based on the empirical likelihood ratio statistic are developed for parameters and for estimating equations, respectively. Finally, Monte Carlo simulations are conducted to demonstrate the performance of proposed estimators.
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This work was partially supported by National Natural Science Foundation of China (Grant No. 10671037) and the Science Foundation of Shanghai Educational Department (Grant No. 06FZ035)
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Sun, S., Zhang, X. Empirical likelihood estimation of discretely sampled processes of OU type. Sci. China Ser. A-Math. 52, 908–931 (2009). https://doi.org/10.1007/s11425-008-0159-z
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DOI: https://doi.org/10.1007/s11425-008-0159-z