Programmer Guide/Command Reference/EVAL/corrfun

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.

See also

avr, dev, var, corrfun

<function list>

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. |}