Estimation for Lévy processes from high frequency data within a long time interval

DOI10.1214/10-AOS856zbMath1215.62084arXiv1105.2424MaRDI QIDQ548536

Valentine Genon-Catalot, Fabienne Comte

Publication date: 29 June 2011

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.2424

zbMATH Keywords

power variationprojection estimatorsadaptive nonparametric estimation

Mathematics Subject Classification ID

Related Items (34)

A note on a fixed-point method for deconvolution ⋮ High-frequency Donsker theorems for Lévy measures ⋮ Nonparametric Bayesian inference for multidimensional compound Poisson processes ⋮ Estimating Gerber-Shiu functions from discretely observed Lévy driven surplus ⋮ Nonparametric estimation of a renewal reward process from discrete data ⋮ Small-time asymptotics of stopped Lévy bridges and simulation schemes with controlled bias ⋮ Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation ⋮ Threshold estimation for a spectrally negative Lévy process ⋮ Estimation of Lévy processes via stochastic programming and Kalman filtering ⋮ Convolution power kernels for density estimation ⋮ Asymptotic equivalence for pure jump Lévy processes with unknown Lévy density and Gaussian white noise ⋮ Nonparametric inference for discretely sampled Lévy processes ⋮ Statistical inference for moving‐average Lévy‐driven processes: Fourier‐based approach ⋮ Adaptive nonparametric estimation for Lévy processes observed at low frequency ⋮ Nonparametric density estimation in compound Poisson processes using convolution power estimators ⋮ Optimally thresholded realized power variations for Lévy jump diffusion models ⋮ Testing the characteristics of a Lévy process ⋮ On non-parametric estimation of the Lévy kernel of Markov processes ⋮ Robust model selection for a semimartingale continuous time regression from discrete data ⋮ Nonparametric implied Lévy densities ⋮ Quantile estimation for Lévy measures ⋮ Spectral-free estimation of Lévy densities in high-frequency regime ⋮ A non-parametric Bayesian approach to decompounding from high frequency data ⋮ Nonparametric estimation for irregularly sampled Lévy processes ⋮ Sup-norm convergence rates for Lévy density estimation ⋮ Weak convergence of the empirical truncated distribution function of the Lévy measure of an Itō semimartingale ⋮ Estimation and Calibration of Lévy Models via Fourier Methods ⋮ Nonparametric estimation for the ruin probability in a Lévy risk model under low-frequency observation ⋮ Bootstrap confidence bands for spectral estimation of Lévy densities under high-frequency observations ⋮ Improved robust model selection methods for a Lévy nonparametric regression in continuous time ⋮ Nonparametric inference on Lévy measures of compound Poisson-driven Ornstein-Uhlenbeck processes under macroscopic discrete observations ⋮ An oracle inequality for penalised projection estimation of Lévy densities from high-frequency observations ⋮ The estimation for Lévy processes in high frequency data ⋮ A Least Squares Estimator for Lévy-driven Moving Averages Based on Discrete Time Observations

Cites Work

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