Correlation Integral

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Correlation Integral

The probability that two points are within a certain distance from one another. Used in the calculation of the correlation dimension.

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BDS Statistic

References in periodicals archive ?

The correlation integral of the embedded time series is defined as follows:

Method of Quantitative Analysis for Multirobot Cooperative Hunting Behaviors

With a properly selected time delay, the considered time series can be reconstructed in the 7M-dimensional phase space by calculating the correlation exponent from the correlation integral (C(r)) as follows:

Nonlinear forecasting of stream flows using a chaotic approach and artificial neural networks

The correlation integral can be rewritten in the form

Separation in data mining based on fractal nature of data

The process used to obtain the fractal dimension is the correlation integral, which compares the proximity of events to one another:

Clustering analysis of AE in rock

The Attractor dimension estimation was accomplished by calculating the correlation integral C(R) (Grassberger and Proccacia, 1983):

Studies on the phase space of multiscale seismicity

Grassberger and Procaccia (1983) and Swinney (1985) use a form of correlation integral to define the CD:

Nonlinearity and low deterministic chaotic behavior in insurance portfolio stock returns

For a given embedding dimension M and a distance [member of], the correlation integral is given by

Nonlinear dependence in gold and silver sutures: Is it chaos?

9 shows log-log plots of the correlation integral against length scale for different embedding dimensions.

FROM INDIVIDUALS TO POPULATION DENSITIES: SEARCHING FOR THE INTERMEDIATE SCALE OF NONTRIVIAL DETERMINISM

C = the Grassberger and Procaccia correlation integral, and

Chaotic dynamics in pacific rim capital markets

m, T]([Epsilon]) = the correlation integral of the finite (T-length) series

Using nonlinear dynamics to test for market efficiency among the major U.S. stock exchanges

The correlation integral for a data series {[[alpha].

Non-linear speculative bubbles in the Pakistani stock market

One of the best DOS system programs available to calculate the correlation integral and BDS statistics can be obtained from W.

Chaos and Order in the Capital Markets: A New View of Cycles, Prices, and Market Volatility