timsac (version 1.3.0)

mulrsp: 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 $i/2$h ($i=0,1,...,$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.

Value

• rspec
  rational spectrum.
• scoh
  simple coherence.

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.

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)