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Title: Noise estimation for ergodic Levy driven SDE in YUIMA package Authors:  Hiroki Masuda - Kyushu University (Japan) [presenting]
Yuma Uehara - The Institute of Statistical Mathematics (Japan)
Lorenzo Mercuri - University of Milan (Italy)
Abstract: Levy driven stochastic differential equation (SDE) is a flexible building block for modeling non-Gaussian high-frequency data observed in many application fields such as biology and ecology. It is, however, common knowledge that a closed form of the likelihood function is rarely available except for quite special cases, making estimation of characteristics of the driving Levy noise difficult. We propose a multistep estimation procedure, by utilizing the Euler residuals constructed from the Gaussian quasi-maximum likelihood estimator (GQMLE); specifically, we first estimate the parametric coefficient by the GQMLE, next approximate unit time increments of the driving noise by partially summing up the Euler residuals, and then apply M-estimation theory (parametric or not). We will present large-sample properties of the proposed estimator, followed by numerical experiments through the YUIMA package in R.