Non parametric threshold estimation for models with stochastic diffusion coefficients and jumps

Details Non parametric threshold estimation for models with stochastic diffusion coefficients and jumps Non parametric threshold estimation for models with stochastic diffusion coefficients and jumps

2006-07-17

arxiv.org/abs/math/0607378v1

Mathematics

Statistics Theory

latex file, 20 pages, 3 figures

Scientific paper

We consider a stochastic process driven by a diffusion and jumps. We devise a technique, which is based on a discrete record of observations, for identifying the times when jumps larger than a suitably defined threshold occurred. The technique allows also jump size estimation. We prove the consistency of a nonparametric estimator of the integrated infinitesimal variance of the process continuous part when the jump component with infinite activity is Levy. Central limit results are proved in the case where the jump component has finite activity. Some simulations illustrate the reliability of the methodology in finite samples.

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