The Brownian semi-stationary (BSS) process was originally proposed by Barndorff-Nielsen and Schmiegel as a modelling framework to describe the temporal turbulent velocity field. This model has several degrees of freedom but a suitable choice of these free parameters is not obvious. In this talk we discuss a specification of these elements and we present some estimation results. We focus in the reproduction of some stylized features of turbulent time series as a way to, partially, validate the model.