Sparse VAR (sparsevar)

Some R functions useful to estimate sparse VAR / VECM models.

Installation

To install the stable version from CRAN:

install.package("sparsevar")

To install the developing version:

install.packages("devtools")
devtools::install_github("svazzole/sparsevar", "master")

Check here to understand which are the dependencies of devtools for your OS.

Quick start

To load the sparsevar package simply type

library(sparsevar)

Using the function included in the package, we simply generate a 20x20 VAR(2) process

set.seed(1)
sim <- simulateVAR(N = 20, p = 2)

This command will generate a model with two sparse matrices with 5% of non-zero entries and a Toeplitz variance-covariance matrix with rho = 0.5. We can estimate the matrices of the process using for example

fit <- fitVAR(sim$series, p = 2, threshold = TRUE)

The results can be seen by plotting the matrices

plotComparisonVAR(sim, fit)

the first row of the plot is made by the matrices of the simulated process and the second row is formed by their estimates.

The fit contains also the estimate of the variance/covariance matrix of the residuals

plotMatrix(fit$sigma)

which can be compared with the covariance matrix of the errors of the generating process

plotMatrix(sim$sigma)

Usage

The functions included for model estimation are:

• fitVAR: to estimate a sparse VAR multivariate time series with ENET, SCAD or MC+;
• fitVECM: to estimate a sparse VECM (Vector Error Correction Model) using LS with penalty (again: ENET, SCAD or MC+);
• impulseResponse: compute the impulse response function;
• errorBands: estimate the error bands for the IRF (using bootstrap);

For simulations:

• simulateVAR: to generate a sparse VAR multivariate time series;
• createSparseMatrix: used to create sparse matrices with a given density;

For plotting:

• plotMatrix: useful to plot matrices and sparse matrices;
• plotVAR: plot all the matrices of the model;
• plotComparisonVAR: plot the comparison between the matrices of the simulated model and the matrices of the estimate.
• plotIRF: plot IRF function;
• plotGridIRF: multiple plots of IRF.

References

[1] Basu, Sumanta; Michailidis, George. Regularized estimation in sparse high-dimensional time series models. Ann. Statist. 43 (2015), no. 4, 1535--1567. doi:10.1214/15-AOS1315.