Identifying the successive Blumenthal-Getoor indices of a discretely observed process

DOI10.1214/12-AOS976zbMath1297.62051arXiv1209.5170OpenAlexW3102284011MaRDI QIDQ693731

Jean Jacod, Yacine Aït-Sahalia

Publication date: 10 December 2012

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

Full work available at URL: https://arxiv.org/abs/1209.5170

zbMATH Keywords

jumpsBrownian motionsemimartingalediscrete samplinghigh frequencyinfinite activityfinite activity

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Markov processes: estimation; hidden Markov models (62M05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Diffusion processes (60J60)

Related Items (15)

Multivariate subordination using generalised gamma convolutions with applications to variance gamma processes and option pricing ⋮ Characterizing financial crises using high-frequency data ⋮ Extensions of Regularity for a Lévy Process ⋮ Estimation of the activity of jumps in time-changed Lévy models ⋮ Estimation of state-dependent jump activity and drift for Markovian semimartingales ⋮ Estimation of mixed fractional stable processes using high-frequency data ⋮ Testing for self-excitation in jumps ⋮ Testing for Jump Spillovers Without Testing for Jumps ⋮ Rate-optimal estimation of the Blumenthal-Getoor index of a Lévy process ⋮ Testing the characteristics of a Lévy process ⋮ Efficient maximum likelihood estimation for Lévy-driven Ornstein-Uhlenbeck processes ⋮ Convergence of extreme values of Poisson point processes at small times ⋮ Identifying the successive Blumenthal-Getoor indices of a discretely observed process ⋮ Estimation and Calibration of Lévy Models via Fourier Methods ⋮ Near-optimal estimation of jump activity in semimartingales

Cites Work

• Nonparametric tests for pathwise properties of semimartingales
• Nonparametric estimation for Lévy processes from low-frequency observations
• Testing whether jumps have finite or infinite activity
• Identifying the successive Blumenthal-Getoor indices of a discretely observed process
• Estimating the degree of activity of jumps in high frequency data
• Spectral estimation of the fractional order of a Lévy process
• Tempering stable processes
• Nonparametric estimation and testing time-homogeneity for processes with independent incre\-ments
• Testing for jumps in a discretely observed process
• Nonparametric estimation for pure jump Lévy processes based on high frequency data
• Activity signature functions for high-frequency data analysis
• Fisher's Information for Discretely Sampled Lvy Processes
• Risk bounds for the non-parametric estimation of Lévy processes
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