Noise inference for ergodic Lévy driven SDE

Hiroki Masuda, Lorenzo Mercuri, Yuma Uehara

Research output: Contribution to journalArticlepeer-review

Abstract

We study inference for the driving Lévy noise of an ergodic stochastic differential equation (SDE) model, when the process is observed at high-frequency and long time and when the drift and scale coefficients contain finite-dimensional unknown parameters. By making use of the Gaussian quasi-likelihood function for the coefficients, we derive a stochastic expansion for functionals of the unit-time residuals, which clarifies some quantitative effect of plugging in the estimators of the coefficients, thereby enabling us to take several inference procedures for the driving-noise characteristics into account. We also present new classes and methods available in YUIMA for the simulation and the estimation of a Lévy SDE model. We highlight the flexibility of these new advances in YUIMA using simulated and real data.

Original languageEnglish
Pages (from-to)2432-2474
Number of pages43
JournalElectronic Journal of Statistics
Volume16
Issue number1
DOIs
Publication statusPublished - 2022

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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