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### A_CORRELATE

A_CORRELATE

The A_CORRELATE function computes the autocorrelation Px(L) or autocovariance Rx(L) of a sample population X as a function of the lag L.  where x is the mean of the sample population x = (x0, x1, x2, ... , xN-1).

This routine is primarily designed for use in 1-D time-series analysis. The mean is subtracted before correlating. For image processing, methods based on FFT should be used instead if more than a few tens of points exist. For example:

Function AutoCorrelate, X   Temp = FFT(X,-1)   RETURN, FFT(Temp * CONJ(Temp), 1)END

This routine is written in the IDL language. Its source code can be found in the file a_correlate.pro in the lib subdirectory of the IDL distribution.

## Examples

`; Define an n-element sample population:X = [3.73, 3.67, 3.77, 3.83, 4.67, 5.87, 6.70, 6.97, 6.40, 5.57]`
` `
`; Compute the autocorrelation of X for LAG = -3, 0, 1, 3, 4, 8:lag = [-3, 0, 1, 3, 4, 8] result = A_CORRELATE(X, lag)PRINT, result`

IDL prints:

`0.0146185  1.00000  0.810879  0.0146185  -0.325279  -0.151684`

## Syntax

Result = A_CORRELATE(X, Lag [, /COVARIANCE] [, /DOUBLE] )

## Arguments

### X

An n-element integer, single-, or double-precision floating-point vector.

### Lag

An n-element integer vector in the interval [-(n-2), (n-2)], specifying the signed distances between indexed elements of X.

## Keywords

### COVARIANCE

Set this keyword to compute the sample autocovariance rather than the sample autocorrelation.

### DOUBLE

Set this keyword to force the computation to be done in double-precision arithmetic.

## Version History

 4 Introduced

## Resources and References

Wayne A. Fuller, Introduction to Statistical Time Series, Wiley-Interscience, December 1995 (ISBN 978-0471552390).