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Title: Noise estimation for ergodic Levy driven stochastic differential equation model Authors:  Yuma Uehara - The Institute of Statistical Mathematics (Japan) [presenting]
Hiroki Masuda - Kyushu University (Japan)
Abstract: To describe non-Gaussian activity in high frequency data obtained from financial, biological, and technological phenomenon, Levy driven stochastic differential equation model is plausible and used in various fields. However, the closed form of its genuine likelihood is not generally given, and thus the information of its driving noise (Levy process) is difficult to be estimated from observed data. To solve such a problem, we propose a new method based on Euler residuals constructed by Gaussian quasi-likelihood estimator: we approximate unit time increments of the driving noise by summing up the corresponding Euler residuals, and making use of them, we can conduct parametric estimation methods of the driving noise with bias correction. We will also present numerical experiments to see the performance of our methods.