AbsoluteCorrelation

AbsoluteCorrelation[v1,v2]

gives the absolute correlation between the vectors v1 and v2.

AbsoluteCorrelation[m]

gives the absolute correlation matrix for the matrix m.

AbsoluteCorrelation[m1,m2]

gives the absolute correlation matrix for the matrices m1 and m2.

AbsoluteCorrelation[dist]

gives the absolute correlation matrix for the multivariate symbolic distribution dist.

AbsoluteCorrelation[dist,i,j]

gives the (i,j)^(th) absolute correlation for the multivariate symbolic distribution dist.

Details

Examples

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Basic Examples  (3)

Absolute correlation between two vectors:

Absolute correlation matrix for a matrix:

Absolute correlation matrix for two matrices:

Scope  (10)

Data  (6)

Exact input yields exact output:

Approximate input yields approximate output:

Absolute correlation between vectors of complexes:

Works with large arrays:

SparseArray data can be used:

Works with data involving quantities:

Distributions and Processes  (4)

Absolute correlation for a continuous multivariate distribution:

Absolute correlation for a discrete multivariate distribution:

Absolute correlation for derived distributions:

Data distribution:

Absolute correlation matrix for a random process at times s and t:

Applications  (3)

Compute the absolute correlation of two financial time series:

AbsoluteCorrelation can be used to measure linear association:

AbsoluteCorrelation can only detect monotonic relationships:

HoeffdingD can be used to detect a variety of dependence structures:

Properties & Relations  (8)

The absolute correlation matrix is symmetric and positive semidefinite:

Covariance and AbsoluteCorrelation are the same for a distribution with zero mean:

Correlation and AbsoluteCorrelation agree for zero mean and unit marginal variances:

AbsoluteCorrelationFunction is the off-diagonal entry in the absolute correlation matrix:

AbsoluteCorrelationFunction for a list can be calculated using absolute correlation:

Calculate absolute correlation function for the data:

Use absolute correlation:

The absolute correlation tends to be large only on the diagonal of a random matrix:

The absolute correlation of a list with itself is proportional to the second moment:

The diagonal of an absolute correlation matrix is the second moment:

Neat Examples  (1)

Compute the absolute correlation for a LCM array:

Wolfram Research (2012), AbsoluteCorrelation, Wolfram Language function, https://reference.wolfram.com/language/ref/AbsoluteCorrelation.html.

Text

Wolfram Research (2012), AbsoluteCorrelation, Wolfram Language function, https://reference.wolfram.com/language/ref/AbsoluteCorrelation.html.

CMS

Wolfram Language. 2012. "AbsoluteCorrelation." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AbsoluteCorrelation.html.

APA

Wolfram Language. (2012). AbsoluteCorrelation. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AbsoluteCorrelation.html

BibTeX

@misc{reference.wolfram_2023_absolutecorrelation, author="Wolfram Research", title="{AbsoluteCorrelation}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/AbsoluteCorrelation.html}", note=[Accessed: 29-November-2023 ]}

BibLaTeX

@online{reference.wolfram_2023_absolutecorrelation, organization={Wolfram Research}, title={AbsoluteCorrelation}, year={2012}, url={https://reference.wolfram.com/language/ref/AbsoluteCorrelation.html}, note=[Accessed: 29-November-2023 ]}