R: Simulate a multivariate autoregressive time series

rar {freqdom}

R Documentation

Simulate a multivariate autoregressive time series

Description

Generates a zero mean vector autoregressive process of a given order.

Usage

rar(
  n,
  d = 2,
  Psi = NULL,
  burnin = 10,
  noise = c("mnormal", "mt"),
  sigma = NULL,
  df = 4
)

Arguments

`n`	number of observations to generate.
`d`	dimension of the time series.
`Psi`	array of `p \geq 1` coefficient matrices. `Psi[,,k]` is the `k`-th coefficient. If no value is set then we generate a vector autoregressive process of order 1. Then, `Psi[,,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.
`burnin`	an integer `\geq 0`. It specifies a number of initial observations to be trashed to achieve stationarity.
`noise`	`mnormal` for multivariate normal noise or `mt` for multivariate student t noise. If not specified `mnormal` is chosen.
`sigma`	covariance or scale matrix of the innovations. By default the identity matrix.
`df`	degrees of freedom if `noise = "mt"`.

Details

We simulate a vector autoregressive process

X_t=\sum_{k=1}^p \Psi_k X_{t-k}+\varepsilon_t,\quad 1\leq t\leq n.

The innovation process \varepsilon_t is either multivariate normal or multivariate 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. To initialise the process we set [X_{1-p},\ldots,X_{0}]=[\varepsilon_{1-p},\ldots,\varepsilon_{0}]. When burnin is set equal to K then, n+K observations are generated and the first K will be trashed.

Value