  In this paper we perform a statistical analysis of the high-frequency returns
of the IBEX35 Madrid stock exchange index. We find that its probability
distribution seems to be stable over different time scales, a stylized fact
observed in many different financial time series. However, an in-depth analysis
of the data using maximum likelihood estimation and different goodness-of-fit
tests rejects the L\'evy-stable law as a plausible underlying probabilistic
model. The analysis shows that the Normal Inverse Gaussian distribution
provides an overall fit for the data better than any of the other subclasses of
the family of the Generalized Hyperbolic distributions and certainly much
better than the L\'evy-stable laws. Furthermore, the right (resp. left) tail of
the distribution seems to follow a power-law with exponent \alpha=4.60 (resp.
\alpha =4.28). Finally, we present evidence that the observed stability is due
to temporal correlations or non-stationarities of the data.
