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, nrow = 1000, ncol = 2)
    x[, 1] <- xorg[1:1000]
    x[, 2] <- xorg[4:1003] + 0.5*rnorm(1000)
    aaa <- ar(x)
    mulrsp(h = 20, d = 2, cov = aaa$var.pred, ar = aaa$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), nrow = 3, ncol = 3, byrow = TRUE)
    ar[, , 2] <- matrix(c(0,  -0.3,  0.5,
                          0.7, -0.4,  1,
                          0,   -0.5,  0.3), nrow = 3, ncol = 3, byrow = TRUE)
    x <- matrix(rnorm(200*3), nrow = 200, ncol = 3)
    y <- mfilter(x, ar, "recursive")
    z <- fpec(y, max.order = 10)
    mulrsp(h = 20, d = 3, cov = z$perr, ar = z$arcoef)

[Package timsac version 1.3.6 Index]