timsac (version 1.3.0)

mulfrf: Frequency Response Function (Multiple Channel)

Description

Compute multiple frequency response function, gain, phase, multiple coherency, partial coherency and relative error statistics.

Usage

mulfrf(y, lag=NULL, iovar=NULL)

Arguments

y

a multivariate time series.

lag

maximum lag. Default is $2 \sqrt{n}$, where $n$ is the number of rows in y.

iovar

input variables (iovar[i], i=1,k) and output variable (iovar[k+1]) ($1 \le k \le d$), where $d$ is the number of columns in y. Default is $c(1:d)$.

Value

• cospec
  spectrum (complex).
• freqr
  frequency response function : real part.
• freqi
  frequency response function : imaginary part.
• gain
  gain.
• phase
  phase.
• pcoh
  partial coherency.
• errstat
  relative error statistics.
• mcoh
  multiple coherency.

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")
  mulfrf(y, lag=20)