Simulate VAR model

This function can (and should) be used to generate a VAR process of any order.

Usage

simulateVAR(N = 100, p = 1, nobs = 250, rho = 0.5, sparsity = 0.05, mu = 0, method = "normal", covariance = "Toeplitz")

where the parameters are

• N: the dimension of the VAR model (default N = 100);
• p: the order of the VAR model (default p = 1);
• nobs: the number of observation for the series (default nobs = 250);
• rho: the intensity of the variance/covariance matrix;
• sparsity: the percentage of non-zero elements in every matrix of the model (default sparsity = 0.05);
• mu: an N vector for the mean of the process (default mu = 0);
• method: the distribution used to generate the non-zero entries for the matrices of the VAR. Possible values are normal, bimodal (default method = "normal");
• covariance: the type of variance/covariance matrix for the process. Possible values are: block1, block2, Toeplitz, Wishart, diagonal(default covariance = "Toeplitz").

Output

The output of the command

sim <- simulateVAR()

is an S3 object (or, if you want, a list), with attr(*, "class") = "var" and attr(*, "type") = "simulation", containing the following elements:

• A: it is a list of p square matrices of dimension N;
• series: an nobs x N matrix containing the simulated series;
• sigma: the variance/covariance matrix of the process;
• noises: the nobs x N matrix of the errors.

Example

In the following we will see how to create a (random) VAR model that can be used for testing pourposes. First we initialize the random seed to 0 and then we create a VAR(2) model with dimension N = 35, sparsity = 0.25 and covariance = "block2".

set.seed(0)
sim <- simulateVAR(N = 35, p = 2, sparsity = 0.25, covariance = "block2")

To see the results, simply plot the VAR matrices and the variance/covariance matrix.

plotVAR(sim)
plotMatrix(sim$sigma)