R: Multiple Rational Spectrum

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/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.

### 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]