# 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.
References in periodicals archive ?
Residuals of this estimated fundamental time series are then tested for possible speculative deviations using a Hamilton regime switching test and a rescaled range Hurst coefficient test, with a further test for nonlinearity beyond the ARCH effects using the BDS statistic.
For large samples, the BDS statistic has a standard normal limiting distribution under the null of i.
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.
The authors then applied three types of analysis (calculation of the Lyapunov exponents (algorithm of Wolf, Swinney & Vastano, 1985), the correlation dimension (method of Grassberger & Procaccia, 1983) and the BDS statistic to the first three series (the fourth had an insufficient number of data) and found that the biomedical innovations showed chaotic dynamics in their initial phases, prior to market entry, with respect to actions and results; however, this was not the case for contextual events, which showed random behavior.
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).
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.
A brief description of the development of the BDS statistic and the concept of the Grassberger and Procaccia correlation dimension, a useful tool is provided in Appendix A.
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.
MBDS statistic, which is a modification of BDS statistic, alSO accepted the null hypothesis.
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