Efficient estimation of stable Lévy process with symmetric jumps

Alexandre Brouste () and Hiroki Masuda ()
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Alexandre Brouste: Le Mans Université Avenue Olivier Messiaen
Hiroki Masuda: Kyushu University

Statistical Inference for Stochastic Processes, 2018, vol. 21, issue 2, No 3, 289-307

Abstract: 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.

Date: 2018
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DOI: 10.1007/s11203-018-9181-0

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