Efficient estimation of stable Lévy process with symmetric jumps

Alexandre Brouste, Hiroki Masuda

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Efficient estimation of a non-Gaussian stable Lévy process with drift and symmetric jumps observed at high frequency is considered. For this statistical experiment, the local asymptotic normality of the likelihood is proved with a non-singular Fisher information matrix through the use of a non-diagonal norming matrix. The asymptotic normality and efficiency of a sequence of roots of the associated likelihood equation are shown as well. Moreover, we show that a simple preliminary method of moments can be used as an initial estimator of a scoring procedure, thereby conveniently enabling us to bypass numerically demanding likelihood optimization. Our simulation results show that the one-step estimator can exhibit quite similar finite-sample performance as the maximum likelihood estimator.

Original languageEnglish
Pages (from-to)289-307
Number of pages19
JournalStatistical Inference for Stochastic Processes
Volume21
Issue number2
DOIs
Publication statusPublished - Jul 1 2018

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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