BDS Statistic

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.
Copyright © 2012, Campbell R. Harvey. All Rights Reserved.
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For large samples, the BDS statistic has a standard normal limiting distribution under the null of i.i.d.
The BDS statistic is proposed by Brock, Dechert and Scheinkman (1987), which is based on the correlation integral that has been quite robust in discerning various types of nonlinearity as well as deterministic chaos.
And then, we perform the noise reduction analysis for the noise added chaotic series by using two filtering techniques and investigate the noise cancellation capabilities of the techniques by the attractor of the series and by the BDS statistic [29-39].
The BDS statistic applied to the standardized re siduals of exponential generalized auto regressive conditional heteroskedasticity (EGARCH) models strongly rejects the null of independent and identically distributed, indicating that conditional heteroskedasticity is not responsible for the presence of the nonlinear structures in the data.
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.
One of the more popular statistical procedures that has evolved from recent progress in chaos theory is the BDS statistic, developed by Brock et al.
We also used the BDS statistic devised by Brock, Dechert and Scheinkman (1987).
The critical values for the BDS statistic of the standardized residuals are developed by bootstrapping the null distribution and reported in Appendix 1.