  In this paper we investigate the parametric inference for the linear
fractional stable motion in high and low frequency setting. The symmetric
linear fractional stable motion is a three-parameter family, which constitutes
a natural non-Gaussian analogue of the scaled fractional Brownian motion. It is
fully characterised by the scaling parameter $\sigma>0$, the self-similarity
parameter $H \in (0,1)$ and the stability index $\alpha \in (0,2)$ of the
driving stable motion. The parametric estimation of the model is inspired by
the limit theory for stationary increments L\'evy moving average processes that
has been recently studied in \cite{BLP}. More specifically, we combine
(negative) power variation statistics and empirical characteristic functions to
obtain consistent estimates of $(\sigma, \alpha, H)$. We present the law of
large numbers and some fully feasible weak limit theorems.
