mulrsp: Multiple Rational Spectrum

In timsac: Time Series Analysis and Control Package

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, ...)

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.
...	graphical arguments passed to plot.specmx.

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. An object of class "specmx".
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)

# 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)

timsac documentation built on Sept. 30, 2023, 5:06 p.m.