# rARMA: Simulate vARMA(2,2) time series In pdSpecEst: An Analysis Toolbox for Hermitian Positive Definite Matrices

## Description

`rARMA` generates `d`-dimensional time series observations from a vARMA(2,2) (vector-autoregressive-moving-average) process based on Gaussian white noise for testing and simulation purposes.

## Usage

 `1` ```rARMA(n, d, Phi, Theta, Sigma, burn = 100, freq = NULL) ```

## Arguments

 `n` number of time series observations to be generated. `d` dimension of the multivariate time series. `Phi` a (d, d, 2)-dimensional array, with `Phi[, , 1]` and `Phi[, , 2]` the autoregressive (AR) coefficient matrices. `Theta` a (d, d, 2)-dimensional array, with `Theta[, , 1]` and `Theta[, , 2]` the moving-average (MA) coefficient matrices. `Sigma` the covariance matrix of the Gaussian white noise component. `burn` a burn-in period when generating the time series observations, by default `burn = 100`. `freq` an optional vector of frequencies, if `!is.null(freq)` the function also returns the underlying Fourier spectral matrix of the stationary generating process evaluated at the frequencies in `freq`.

## Value

The function returns a list with two components:

 `X ` generated time series observations, the `d` columns correspond to the components of the multivariate time series. `f ` if `!is.null(freq)`, `f` is a `(d, d, length(freq))`-dimensional array corresponding to the underlying Fourier spectral matrix curve of (d,d)-dimensional HPD matrices evaluated at the frequencies in `freq`. If `is.null(freq)`, `f` is set to `NULL`.

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## Examples

 ```1 2 3 4 5 6 7``` ```## ARMA(1,1) process: Example 11.4.1 in (Brockwell and Davis, 1991) freq <- seq(from = pi / 100, to = pi, length = 100) Phi <- array(c(0.7, 0, 0, 0.6, rep(0, 4)), dim = c(2, 2, 2)) Theta <- array(c(0.5, -0.7, 0.6, 0.8, rep(0, 4)), dim = c(2, 2, 2)) Sigma <- matrix(c(1, 0.71, 0.71, 2), nrow = 2) ts.sim <- rARMA(200, 2, Phi, Theta, Sigma, freq = freq) ts.plot(ts.sim\$X) # plot generated time series traces. ```

pdSpecEst documentation built on Jan. 8, 2020, 5:08 p.m.