rma {freqdom}

Moving average process

Description

Generates a zero mean vector moving average process.

Usage

rma(n, d = 2, Psi = NULL, noise = c("mnormal", "mt"), sigma = NULL, df = 4)

Arguments

n

number of observations to generate.

d

dimension of the time series.

Psi

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.

noise

mnormal for multivariate normal noise or mt for multivariate t noise. If not specified mnormal is chosen.

sigma

covariance or scale matrix of the innovations. If NULL then the identity matrix is used.

df

degrees of freedom if noise = "mt".

Details

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.

Value

A matrix with d columns and n rows. Each row corresponds to one time point.

See Also

rar