Jump filtering and efficient drift estimation for Lévy-driven SDEs

DOI10.1214/17-AOS1591zbMath1430.60066arXiv1603.05290OpenAlexW2962793781MaRDI QIDQ2413596

Dasha Loukianova, Arnaud Gloter, Hilmar Mai

Publication date: 14 September 2018

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

Full work available at URL: https://arxiv.org/abs/1603.05290

zbMATH Keywords

maximum likelihood estimationhigh frequency dataergodic propertiesLévy-driven SDEefficient drift estimation

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Markov processes: estimation; hidden Markov models (62M05) Jump processes on discrete state spaces (60J74)

Related Items

Convoluted smoothed kernel estimation for drift coefficients in jump-diffusion models ⋮ Estimation of state-dependent jump activity and drift for Markovian semimartingales ⋮ Parameter estimation of discretely observed interacting particle systems ⋮ Unbiased truncated quadratic variation for volatility estimation in jump diffusion processes ⋮ Local asymptotic normality for ergodic jump-diffusion processes via transition density approximation ⋮ Threshold estimation for jump-diffusions under small noise asymptotics ⋮ On a projection least squares estimator for jump diffusion processes ⋮ Rate-optimal estimation of the Blumenthal-Getoor index of a Lévy process ⋮ Pairs trading with a mean-reverting jump–diffusion model on high-frequency data ⋮ Estimating functions for jump-diffusions ⋮ Drift estimation for a Lévy-driven Ornstein-Uhlenbeck process with heavy tails ⋮ Non parametric estimation of the diffusion coefficients of a diffusion with jumps ⋮ Joint estimation for volatility and drift parameters of ergodic jump diffusion processes via contrast function

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Jump-Diffusion Model for Option Pricing
• The Morris-Lecar neuron model embeds a leaky integrate-and-fire model
• Convergence of Gaussian quasi-likelihood random fields for ergodic Lévy driven SDE observed at high frequency
• The speed of convergence of the threshold estimator of integrated variance
• Quasi-likelihood analysis for the stochastic differential equation with jumps
• Interchanging the order of differentiation and stochastic integration
• \(M\)-estimation for discretely observed ergodic diffusion processes with infinitely many jumps
• Estimation of parameters for diffusion processes with jumps from discrete observations
• Ergodicity and exponential \(\beta\)-mixing bounds for multidimensional diffusions with jumps
• Erratum to: ``Ergodicity and exponential \(\beta \)-mixing bound for multidimensional diffusions with jumps
• Estimation for diffusion processes from discrete observation
• On the estimation of the diffusion coefficient for multi-dimensional diffusion processes
• A note on limit theorems for multivariate martingales
• Approximate self-weighted LAD estimation of discretely observed ergodic Ornstein-Uhlenbeck processes
• Econometrics of co-jumps in high-frequency data with noise
• Optimally thresholded realized power variations for Lévy jump diffusion models
• Efficient maximum likelihood estimation for Lévy-driven Ornstein-Uhlenbeck processes
• Uniform law of large numbers and consistency of estimators for Harris diffusions
• Non-Gaussian Ornstein–Uhlenbeck-based Models and Some of Their Uses in Financial Economics
• A Practical Inference for Discretely Observed Jump-diffusions from Finite Samples
• Approximate discrete-time schemes for statistics of diffusion processes
• Asymptotic Statistics
• Estimation of an Ergodic Diffusion from Discrete Observations
• Financial Modelling with Jump Processes
• Option pricing when underlying stock returns are discontinuous