mulrsp {timsac}R Documentation

Multiple Rational Spectrum

Description

Compute rational spectrum for d-dimensional ARMA process.

Usage

mulrsp(h, d, cov, ar=NULL, ma=NULL, log=FALSE, plot=TRUE,
       plot.scale=FALSE)

Arguments

h

specify frequencies i/2h (i=0,1,...,h).

d

dimension of the observation vector.

cov

covariance matrix.

ar

coefficient matrix of autoregressive model. ar[i,j,k] shows the value of i-th row, j-th column, k-th order.

ma

coefficient matrix of moving average model. ma[i,j,k] shows the value of i-th row, j-th column, k-th order.

log

logical. If TRUE rational spectrums rspec are plotted as log(rspec).

plot

logical. If TRUE rational spectrums rspec are plotted.

plot.scale

logical. IF TRUE the common range of the y-axis is used.

Details

ARMA process :

y(t) - A(1)y(t-1) -...- A(p)y(t-p) = u(t) - B(1)u(t-1) -...- B(q)u(t-q)

where u(t) is a white noise with zero mean vector and covariance matrix cov.

Value

rspec

rational spectrum.

scoh

simple coherence.

References

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

Examples

  # Example 1 for the normal distribution
  xorg <- rnorm(1003)
  x <- matrix(0,1000,2)
  x[,1] <- xorg[1:1000]
  x[,2] <- xorg[4:1003]+0.5*rnorm(1000)
  aaa <- ar(x)
  mulrsp(20, 2, aaa$var.pred, aaa$ar, plot=TRUE, plot.scale=TRUE)

  # Example 2 for the AR model
  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")
  z <- fpec(y, 10)
  mulrsp(20, 3, z$perr, z$arcoef)
[Package timsac version 1.3.5 Index]