sparsevar is an R package that estimates sparse VAR and VECM model using penalized least squares methods (PLS): it is possible to use
various penalties such as ENET, SCAD or MC+ penalties. The sparsity parameter can be estimated using cross-validation or time slicing. When using ENET it is possible to estimate VAR(1) of dimension up to 200, while when using one of the other two is better not to go beyond 50. When estimating a VAR(\(p\)) model then the limits are roughly \(200/p\) and \(50/p\), respectively.
The authors of
sparsevar are Monica Billio, Lorenzo Frattarolo and Simone Vazzoler and the R package is mantained by Simone Vazzoler. This vignette describes the usage of
sparsevar in R.
The simplest way to install the package is by using the CRAN repositories, by typing in the R console
install.packages("sparsevar", repos = "http://cran.us.r-project.org")
It is also possible to install the developing version of the package by typing
install.packages("devtools", repos = "http://cran.us.r-project.org") devtools::install_github("svazzole/sparsevar")
To load the
sparsevar package simply type
Using a function included in the package, we simply generate a \(20\times 20\) VAR\((2)\) process
set.seed(1) sim <- simulateVAR(N = 20, p = 2)
and we can estimate the matrices of the process using
fit <- fitVAR(sim$series, p = 2)
The results can be seen by plotting the matrices
fitVAR for VAR model estimation or
fitVECM for VECM estimation.
The common arguments for the two functions are:
data: a matrix containing the multivariate time series (variables in columns, observations in rows);
p: the order of the VAR model to be estimated; default
p = 1for
method: the method used to estimate the sparsity parameter. Default is
method = "cv"(cross-validation). Another possibility is
method = "timeSlice".
penalty: the penalty used in least squares. Possible values are:
...: sequence of options. Some of them depend on the penalty used, some on the method and some are global.
FALSE(default). Parallel cross-validation (on the folds);
parallel = TRUEthen you must specify the number of cores used for the parallelization (default =
nfolds: number of folds to use in the cross validation (default
nfolds = 10)
TRUEall the elements of the VAR/VECM matrices that are small “enough” are set to 0.
penalty = "ENET"
alpha: a value in (0,1) (default
alpha = 1).
alpha = 1is LASSO regression,
alpha = 0is Ridge LS;
nlambda: number of lambdas used for cross validation.
foldsID: the vector containing the IDs for the folds in the cross validation.
penalty = "SCAD"or
eps: convergence tolerance
picassopackage for SCAD estimation.
The output of the function
fitVAR is a S3 object of class
mu: a vector for the mean;
A: a list of length
pcontaining the matrices estimated for the VAR(p) model;
lambda: the estimated sparsity parameter;
mse: the mean square error of the cross validation or time slicing;
time: elapsed time for the estimation;
series: the transformed data matrix (centered or scaled);
residuals: the matrix of the estimated residuals;
sigma: the variance/covariance matrix of the residuals;
penalty: the penalty used (
method: the method used (
simulateVAR. The parameters for the function are:
N: the dimension of the process;
nobs: the number of observations of the process;
rho: the variance/covariance “intensity”;
sparsity: the percentage of non zero elements in the matrix of the VAR;
Use the functions
errorBands to compute the impulse response
function and to estimate the error bands of the model respectively.
irf <- impulseResponse(fit) eb <- errorBandsIRF(fit, irf)
results <- fitVAR(rets)
will estimate VAR(1) process using LASSO regression on the dataset
results <- fitVAR(rets, p = 3, penalty = "ENET", parallel = TRUE, ncores = 5, alpha = 0.95, type.measure = "mae", lambda = "lambda.1se")
will estimate a VAR(3) model on the dataset
rets using the penalty
alpha = 0.95 (between LASSO and Ridge). For the cross validation it will use
"mae" (mean absolute error) insteadof mean square error and it will choose as model the one correspondent to the lambda which is at 1 std deviation from the minimum. Moreover it will parallelize the cross validation over 5 cores.
Here we compute the IRF for the model estimated in the Quick Start section.
irf <- impulseResponse(fit) eb <- errorBandsIRF(fit, irf, verbose = FALSE) plotIRFGrid(irf, eb, indexes = c(11,20))
sim <- simulateVAR(N = 100, nobs = 250, rho = 0.75, sparsity = 0.05, method = "normal")