Efficient estimation of stable Levy process with symmetric jumps

2018/05/23 by Brouste, Alexandre, Masuda, Hiroki · 1 citation
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1805.08926

Abstract

Efficient estimation of a non-Gaussian stable Levy 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.

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