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freqdom (version 2.0.5)

rma: 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)

Value

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

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.

See Also

rar