mulrsp {timsac} | R Documentation |
Compute rational spectrum for d-dimensional ARMA process.
mulrsp(h, d, cov, ar = NULL, ma = NULL, log = FALSE, plot = TRUE, plot.scale = FALSE)
h |
specify frequencies i/2 |
d |
dimension of the observation vector. |
cov |
covariance matrix. |
ar |
coefficient matrix of autoregressive model. |
ma |
coefficient matrix of moving average model. |
log |
logical. If |
plot |
logical. If |
plot.scale |
logical. IF |
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
.
rspec |
rational spectrum. |
scoh |
simple coherence. |
H.Akaike and T.Nakagawa (1988) Statistical Analysis and Control of Dynamic Systems. Kluwer Academic publishers.
# 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)