Efficient estimation of stable Lévy process with symmetric jumps

Alexandre Brouste, Hiroki Masuda

Research output: Contribution to journalArticle

1 Citation (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

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Efficient Estimation
Stable Process
Likelihood
Jump
Local Asymptotic Normality
Estimator
Fisher Information Matrix
Asymptotic Efficiency
Method of Moments
Asymptotic Normality
Scoring
Maximum Likelihood Estimator
Roots
Optimization
Experiment
Simulation

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Cite this

Efficient estimation of stable Lévy process with symmetric jumps. / Brouste, Alexandre; Masuda, Hiroki.

In: Statistical Inference for Stochastic Processes, Vol. 21, No. 2, 01.07.2018, p. 289-307.

Research output: Contribution to journalArticle

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