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Scaling, stability and distribution of the high-frequency returns of theIbex35index

Authors
Journal
Physica A Statistical Mechanics and its Applications
0378-4371
Publisher
Elsevier
Publication Date
Volume
392
Issue
6
Identifiers
DOI: 10.1016/j.physa.2012.11.026
Keywords
  • Financial Time Series
  • High-Frequency Returns
  • Generalized Hyperbolic Distributions
  • Lévy-Stable Distributions
  • Scaling Laws
  • Tail Behavior
Disciplines
  • Mathematics

Abstract

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 Lévy-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 Generalized Hyperbolic distributions and certainly much better than the Lévy-stable laws. Furthermore, the right (resp. left) tail of the distribution seems to follow a power-law with exponent α≈4.60 (resp. α≈4.28). Finally, we present evidence that the observed stability is due to temporal correlations or non-stationarities of the data.

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