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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 equations serve as good candidates. Since the closed form of its genuine likelihood is generally not obtained, the estimation of its driving noise is often done by empirical moment fittings with respect to its Levy measure. However, the measure sometimes takes complex form, and thus intractable. For such a problem, we consider the approximation of unit time increments of the driving noise based on the Euler residual. By making use of this approximation, we can conduct parametric estimation methods of the driving noise with bias correction. We will present its theoretical properties and show some numerical experiments.