  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.
