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BDS Statistic

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BDS Statistic
A statistic based upon the correlation integral which examines the probability that a purely random system could have the same scaling properties as the system under study. See: Correlation Integral.


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First, the level of employment in the BDS data is consistently higher than the level of employment in the BED data, so it would be expected for the BDS statistics to fluctuate by larger numbers of jobs than do the BED statistics.
The critical values for the BDS statistic of the standardized residuals are developed by bootstrapping the null distribution and reported in Appendix 1.
There are three tests that we employ here: the Correlation Dimension of Grassberger and Procaccia (1983), and the BDS statistic of Brock, Deckert, and Scheinkman (1987), and a measure of entropy termed Kolmogorov-Sinai invariant, also known as Kolmogorov entropy.
 
 
 
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