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

2006/07/17 by Cecilia Mancini, Mancini, Cecilia · 3 citations
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Methods and Inference #Statistics Theory (math.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.math/0607378

openalex publication_date 2006/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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