Asymptotic properties of the partition function and applications in tail index inference of heavy-tailed data

Abstract

The so-called partition function is a sample moment statistic based on blocks of data and it is often used in the context of multifractal processes. It will be shown that its behaviour is strongly influenced by the tail of the distribution underlying the data both in independent identically distributed and weakly dependent cases. These results will be used to develop graphical and estimation methods for the tail index of a distribution. The performance of the tools proposed is analysed and compared with other methods by means of simulations and examples.

Keywords:

• heavy tails
• partition function
• scaling function
• tail index

AMS Subject Classifications:

• 62F10
• 62F12
• 62E20

Notes

1. The data can be obtained from: http://www.ma.hw.ac.uk/~mcneil/data.html.