Generates a zero mean vector moving average process.
rma(n, d = 2, Psi = NULL, noise = c("mnormal", "mt"), sigma = NULL, df = 4)
A matrix with d
columns and n
rows. Each row corresponds to one time point.
number of observations to generate.
dimension of the time series.
a timedom
object with operators Psi$operators
, where Psi$operators[,,k]
is the operator on thelag lags[k]
. If no value is set then we generate a vector moving average process
of order \(1\). Then, Psi$lags = c(1)
and Psi$operators[,,1]
is proportional to \(\exp(-(i+j)\colon 1\leq i, j\leq d)\) and such
that the spectral radius of Psi[,,1]
is \(1/2\).
mnormal
for multivariate normal noise or mt
for multivariate \(t\) noise. If not specified mnormal
is chosen.
covariance or scale matrix of the innovations. If NULL then the identity matrix is used.
degrees of freedom if noise = "mt"
.
This simulates a vector moving average process
$$
X_t=\varepsilon_t+\sum_{k \in lags} \Psi_k \varepsilon_{t-k},\quad 1\leq t\leq n.
$$
The innovation process \(\varepsilon_t\) is either multivariate normal or multivarite \(t\) with
a predefined covariance/scale matrix sigma and zero mean. The noise is generated with the
package mvtnorm
. For Gaussian noise we use rmvnorm
. For Student-t noise we use
rmvt
. The parameters sigma
and df
are imported as arguments, otherwise we use default settings.
rar