Limit theorems for power variations of pure-jump processes with application to activity estima\-tion

DOI10.1214/10-AAP700zbMath1215.62088arXiv1104.1064OpenAlexW3122888083MaRDI QIDQ535202

Viktor Todorov, George Tauchen

Publication date: 11 May 2011

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

Full work available at URL: https://arxiv.org/abs/1104.1064

zbMATH Keywords

jumpscentral limit theoremhigh-frequency dataBlumenthal-Getoor indexrealized power variationItô semimartingaleactivity index

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) Generalizations of martingales (60G48) Diffusion processes (60J60)

Related Items (22)

Trading-flow assisted estimation of the jump activity index ⋮ Nonparametric inference on Lévy measures and copulas ⋮ Joint estimation for SDE driven by locally stable Lévy processes ⋮ How precise is the finite sample approximation of the asymptotic distribution of realised variation measures in the presence of jumps? ⋮ Realized Laplace transforms for pure-jump semimartingales ⋮ Nonparametric inference for the spectral measure of a bivariate pure-jump semimartingale ⋮ Power variation from second order differences for pure jump semimartingales ⋮ Large deviations of realized volatility ⋮ Higher-order small time asymptotic expansion of Itô semimartingale characteristic function with application to estimation of leverage from options ⋮ Limit theorems for integrated local empirical characteristic exponents from noisy high-frequency data with application to volatility and jump activity estimation ⋮ Laws of large numbers for Hayashi-Yoshida-type functionals ⋮ On simulation of tempered stable random variates ⋮ Efficient estimation of integrated volatility in presence of infinite variation jumps ⋮ Jump activity estimation for pure-jump semimartingales via self-normalized statistics ⋮ On the jump activity index for semimartingales ⋮ A local stable bootstrap for power variations of pure-jump semimartingales and activity index estimation ⋮ Inference for local distributions at high sampling frequencies: a bootstrap approach ⋮ Limit theorems for the empirical distribution function of scaled increments of Itô semimartingales at high frequencies ⋮ INFERENCE FOR OPTION PANELS IN PURE-JUMP SETTINGS ⋮ Estimating functions for SDE driven by stable Lévy processes ⋮ Testing for pure-jump processes for high-frequency data ⋮ The fine structure of equity-index option dynamics

Cites Work

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