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Non‐parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps
Author(s) -
MANCINI CECILIA
Publication year - 2009
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2008.00622.x
Subject(s) - mathematics , estimator , jump , parametric statistics , jump process , stochastic volatility , parametric model , jump diffusion , volatility (finance) , diffusion process , diffusion , statistical physics , statistics , econometrics , computer science , knowledge management , physics , innovation diffusion , quantum mechanics , thermodynamics
. We consider a stochastic process driven by diffusions and jumps. Given a discrete record of observations, we devise a technique for identifying the times when jumps larger than a suitably defined threshold occurred. This allows us to determine a consistent non‐parametric estimator of the integrated volatility when the infinite activity jump component is Lévy. Jump size estimation and central limit results are proved in the case of finite activity jumps. Some simulations illustrate the applicability of the methodology in finite samples and its superiority on the multipower variations especially when it is not possible to use high frequency data.