xcov function

Cross-covariance

Compute covariance at various lags (= correlation(x-mean(x), y-mean(y))).

xcov(
  x,
  y = NULL,
  maxlag = if (is.matrix(x)) nrow(x) - 1 else max(length(x), length(y)) - 1,
  scale = c("none", "biased", "unbiased", "coeff")
)

Arguments

• x: Input, numeric or complex vector or matrix. Must not be missing.

• y: Input, numeric or complex vector data. If x is a matrix (not a vector), y must be omitted. y may be omitted if x is a vector; in this case xcov estimates the autocovariance of x.

• maxlag: Integer scalar. Maximum covariance lag. If omitted, the default value is N-1, where N is the greater of the lengths of x and y or, if x is a matrix, the number of rows in x.

• scale: Character string. Specifies the type of scaling applied to the covariation vector (or matrix). matched to one of:

  • "none": return the unscaled covariance, C
  • "biased": return the biased average, C/N
  • "unbiased": return the unbiased average, C(k)/(N-|k|)
  • "coeff": return C/(covariance at lag 0)

  If omitted, the default value is "none". If y is supplied but does not have the same length as x, scale must be "none".

Returns

A list containing the following variables:

• C: array of covariance estimates
• lags: vector of covariance lags [-maxlag:maxlag]

The array of covariance estimates has one of the following forms:

1. Cross-covariance estimate if X and Y are vectors.
2. Autocovariance estimate if is a vector and Y is omitted.
3. If x is a matrix, C is a matrix containing the cross-covariance estimates of each column with every other column. Lag varies with the first index so that C has 2 * maxlag + 1 rows and $P^2$ columns where P is the number of columns in x.

Examples

N <- 128
fs <- 5
t <- seq(0, 1, length.out = N)
x <- sin(2 * pi * fs * t) + runif(N)
cl <- xcov(x, maxlag = 20, scale = 'coeff')
plot (cl$lags, cl$C, type = "h", xlab = "", ylab = "")
points (cl$lags, cl$C)
abline(h = 0)

See Also

xcorr.

Author(s)

Paul Kienzle, pkienzle@users.sf.net .

Conversion to R by Geert van Boxtel, G.J.M.vanBoxtel@gmail.com .