# AbsoluteCorrelation

AbsoluteCorrelation[v,w]

gives the absolute correlation between the vectors v and w.

AbsoluteCorrelation[a,b]

gives the absolute cross-correlation matrix for the matrices a and b.

gives the absolute correlation matrix for the matrix a.

AbsoluteCorrelation[dist]

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

AbsoluteCorrelation[dist,i,j]

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

# 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:

A structured array can be used (see the guide):

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 the second moment:

For random data:

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 (updated 2023).

#### Text

Wolfram Research (2012), AbsoluteCorrelation, Wolfram Language function, https://reference.wolfram.com/language/ref/AbsoluteCorrelation.html (updated 2023).

#### CMS

Wolfram Language. 2012. "AbsoluteCorrelation." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. 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_2024_absolutecorrelation, author="Wolfram Research", title="{AbsoluteCorrelation}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/AbsoluteCorrelation.html}", note=[Accessed: 25-April-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_absolutecorrelation, organization={Wolfram Research}, title={AbsoluteCorrelation}, year={2023}, url={https://reference.wolfram.com/language/ref/AbsoluteCorrelation.html}, note=[Accessed: 25-April-2024 ]}