Scaling, stability and distribution of the high-frequency returns of the IBEX35 index

TL;DR

This study analyzes high-frequency IBEX35 index returns, finding stable distributional features over time, with the Normal Inverse Gaussian distribution fitting best, and tail behaviors following power-laws, influenced by temporal correlations.

Contribution

It demonstrates that the Normal Inverse Gaussian distribution models IBEX35 returns better than Lévy-stable laws and reveals tail power-law behaviors linked to data correlations.

Findings

Normal Inverse Gaussian fits data better than Lévy-stable laws

Distribution remains stable across different time scales

Tail exponents suggest power-law decay in extreme returns

Abstract

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.