Least squares estimators for discretely observed stochastic processes driven by small Lévy noises

Hongwei Long, Yasutaka Shimizu, Wei Sun

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small Lévy noises. We do not impose any moment condition on the driving Lévy process. Under certain regularity conditions on the drift function, we obtain consistency and rate of convergence of the least squares estimator (LSE) of the drift parameter when a small dispersion coefficient ε → 0 and n → ∞ simultaneously. The asymptotic distribution of the LSE in our general setting is shown to be the convolution of a normal distribution and a distribution related to the jump part of the Lévy process. Moreover, we briefly remark that our methodology can be easily extended to the more general case of semi-martingale noises.

Original languageEnglish
Pages (from-to)422-439
Number of pages18
JournalJournal of Multivariate Analysis
Volume116
DOIs
Publication statusPublished - 2013 Apr 1
Externally publishedYes

Keywords

  • Asymptotic distribution of LSE
  • Consistency of LSE
  • Discrete observations
  • Least squares method
  • Parameter estimation
  • Small Lévy noises
  • Stochastic processes

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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