Programmer Guide/Command Reference/EVAL/corrfun: Difference between revisions
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{{DISPLAYTITLE:{{SUBPAGENAME}}}} | {{DISPLAYTITLE:{{SUBPAGENAME}}}} | ||
Compute the autocorrelation or cross-correlation function. | Compute the autocorrelation or cross-correlation function. | ||
---- | |||
;Usage: | |||
:{|class="keinrahmen" | |||
|'''<code>corrfun(''x''<sub>vector</sub> {, ''n'' {, ''scale''}})</code>''' | |||
| ... autocorrelation of ''x'' | |||
|- | |||
|'''<code>corrfun(''x''<sub>vector</sub>, ''y''<sub>vector</sub> {, ''n'' {, ''scale''}})</code>''' | |||
| ... cross correlation of ''x'' and ''y'' | |||
|} | |||
:;''x'', ''y'': data vectors | |||
:;''n'': the number of lags; 0 < n < <code>ncol(''x'')</code> (default=<code>ncol(''x'')/2</code>) | |||
:;''scale'': specifies the scaling of the function: | |||
::{|class=keinrahmen" | |||
|''scale=0'' ||... no scaling (default) | |||
|''scale=1'' ||... "biased", each lag ''i'' is scaled by the length of ''x'' (<code>1/ncol(''x'')</code>) | |||
|''scale=2'' ||... "unbiased", each lag ''i'' is scaled by the number of correlated elements (<code>1/(ncol(''x'')-1)</code>) | |||
;Result 1: The correlecation coefficient ''r'' (product-moment correlation) of the vectors ''x'' and ''y''. | |||
:<code>''r'' = var(''x'', ''y'') / sqrt( var(''x'') * var(''y'') )</code> | |||
---- | ---- | ||
;Usage 1: '''<code>var(''x''<sub>vector</sub>, ''y''<sub>vector</sub>)</code>''' | ;Usage 1: '''<code>var(''x''<sub>vector</sub>, ''y''<sub>vector</sub>)</code>''' | ||
Revision as of 14:21, 8 April 2011
Compute the autocorrelation or cross-correlation function.
- Usage
corrfun(xvector {, n {, scale}})... autocorrelation of x corrfun(xvector, yvector {, n {, scale}})... cross correlation of x and y
- x, y
- data vectors
- n
- the number of lags; 0 < n <
ncol(x)(default=ncol(x)/2) - scale
- specifies the scaling of the function:
scale=0 ... no scaling (default) scale=1 ... "biased", each lag i is scaled by the length of x ( 1/ncol(x))scale=2 ... "unbiased", each lag i is scaled by the number of correlated elements ( 1/(ncol(x)-1))- Result 1
- The correlecation coefficient r (product-moment correlation) of the vectors x and y.
r = var(x, y) / sqrt( var(x) * var(y) )
- Usage 1
var(xvector, yvector)- Result 1
- The correlecation coefficient r (product-moment correlation) of the vectors x and y.
r = var(x, y) / sqrt( var(x) * var(y) )
- Usage 2
var(xmatrix)var(xmatrix, yscalar)var(xmatrix, yvector)- Result 2
- The correlation matrix r of the column vectors of x.
r[i,j] = var(x[*,i], x[*,j]) / sqrt( var(x[*,i]) * var(x[*,j]) ) , with: i,j = 0..ncol(x)-1- If the argument y is supplied, it is used as column average like for the computation of the covariance matrix.
corrfun
corrfun(x, lags, scale) lags the number of coefficients def.=nrow(x)/2 scale the scaling def.=0 0=no scaling 1=scaling with "1 / nrow(x)", 2=scaling with "1 / (nrow(x) - lag)" The result is a vector with lags elements.
corrfun(x, y, lags, scale) Calculate the coefficients 0..lags-1 of the cross-correlation function of the vectors x and y. The parameters are the same as for the auto-correlation function.
