timsac (version 1.3.0)

mulnos: Relative Power Contribution

Description

Compute relative power contributions in differential and integrated form, assuming the orthogonality between noise sources.

Usage

mulnos(y, max.order=NULL, control=NULL, manip=NULL, h)

Arguments

y

a multivariate time series.

max.order

upper limit of model order. Default is $2 \sqrt{n}$, where $n$ is the length of time series y.

control

controlled variables. Default is $c(1:d)$, where $d$ is the dimension of the time series y.

manip

manipulated variables. Default number of manipulated variable is $0$.

h

specify frequencies $i/2$h ($i=0,...,$h).

Value

• nperr
  a normalized prediction error covariance matrix.
• diffr
  differential relative power contribution.
• integr
  integrated relative power contribution.

References

H.Akaike and T.Nakagawa (1988) Statistical Analysis and Control of Dynamic Systems. Kluwer Academic publishers.

Examples

ar <- array(0,dim=c(3,3,2))
  ar[,,1] <- matrix(c(0.4,  0,   0.3,
                      0.2, -0.1, -0.5,
                      0.3,  0.1, 0),3,3,byrow=TRUE)
  ar[,,2] <- matrix(c(0,  -0.3,  0.5,
                      0.7, -0.4,  1,
                      0,   -0.5,  0.3),3,3,byrow=TRUE)
  x <- matrix(rnorm(200*3),200,3)
  y <- mfilter(x,ar,"recursive")
  mulnos(y, max.order=10, h=20)