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/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. |
plot.scale |
logical. IF TRUE the common range of the y-axisis is used. |
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(0,1000,2) 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),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, max.order=10, ncon=3, nman=0) mulrsp(h=20, d=3, cov=z$perr, ar=z$arcoef) # d=ncon+nman