An alternative correlation dimension statistic

Abstract

One of the problems plaguing these applications has been the large data requirements of these statistical procedures. Time series numbering 20,000 are common in physical science applications, while results of applications to shorter time series with lengths between 500 and 2,000 -it being difficult enough to obtain such economic data- have suffered from a bias towards low dimensions in the statistical results. The purpose of this paper is to prosent a modified statistic which not only calculates dimension and simultaneously tests for the IID null, but is also not biased towards Iow dimensions and more sensitive to the presence of stochastic structure in the shorter time series mentioned above.