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 > 0, the self-similarity parameter H 2 (0; 1) and the stability index 2 (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 [5]. More specically, we combine (negative) power variation statistics and empirical characteristic functions to obtain consistent estimates of ( ; ;H). We present the law of large numbers and some fully feasible weak limit theorems.