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.
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4) Therefore, under the null hypothesis the BDS statistic
Following Adrangi and Chatrath (2003), we employ three tests: the Correlation Dimension of Grassberger and Procaccia (1983) and Takens (1984), and the BDS statistic of Brock, Dechert, and Scheinkman (1987), and a measure of entropy termed Kohnogorov-Sinai invariant, also known as Kohnogorov entropy.
Aside from its ability to detect nonlinear relationships, the BDS statistic, by its very design, is also sensitive to linear processes.
The BDS statistic also comes from the correlation integral as
The critical values for the BDS statistic of the standardized residuals are developed by bootstrapping the null distribution and reported in Appendix 1.
MBDS statistic, which is a modification of BDS statistic, alSO accepted the null hypothesis.
The BDS statistic, which can be denoted as Wm,T(e) is given by
We deploy two tests of chaos: (i) the Correlation Dimension of Grassberger and Procaccia (1983) and Takens (1984), (ii) and the BDS statistic of Brock, Dechert, and Scheinkman (1987) which are discussed in detail in Adrangi et al.
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 nonlinear dynamics is the BDS statistic, developed by Brock et al.
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.
One of the more popular statistical procedures that has evolved from recent progress in nonlinear dynamics is the BDS statistic, developed by Brock et al (1991), which tests whether a data series is independently and identically distributed (IID).