fitVAR: Fit VAR Model with Elastic Net via Cross Validation

Description

Estimates a (possibly high-dimensional) VAR model using penalized least squares with an elastic net penalty and cross validation. This function is adapted from the sparsevar package (https://github.com/svazzole/sparsevar/tree/master), which is distributed under the GNU General Public License v2. The code has been modified to specifically implement the elastic net penalty (penalty = "ENET") and cross validation (method = "cv").

Usage

fitVAR(data, p = 1, ...)

Value

A list with the following components:

mu: A vector of means for each variable.
A: A list (of length p) of the estimated coefficient matrices for the VAR process.
fit: (Optional) The complete results of the penalized least squares estimation.
lambda: The chosen lambda value (by cross validation).
mse: The minimum mean squared error from cross validation.
mse_sd: The standard deviation of the mean squared error.
time: Elapsed time for the estimation.
series: The (possibly transformed) input time series.
residuals: The residuals of the VAR model.
sigma: The estimated variance/covariance matrix of the residuals.

Arguments

data

A numeric matrix or data frame with time series data (observations in rows, variables in columns).

p

Integer. The order of the VAR model.

...

Additional options for estimation. Global options include:

threshold: Logical. If TRUE, all entries smaller than the oracle threshold are set to zero.
scale: Logical. Whether to scale the data (default is FALSE).
nfolds: Integer. The number of folds used for cross validation (default is 10).
parallel: Logical. If TRUE, use multicore backend (default is FALSE).
ncores: Integer. If parallel = TRUE, specify the number of cores to use.
alpha: Numeric. The elastic net mixing parameter (default is 1, i.e. LASSO).
type.measure: Character. The error measure for CV (e.g., "mse" or "mae").
nlambda: Integer. The number of lambda values to use in cross validation (default is 100).
leaveOut: Integer. In time slice validation, leave out the last observations (default is 15).
horizon: Integer. The forecast horizon to use for estimating error (default is 1).
lambda: Either a numeric vector of lambda values or a string indicating which lambda to use (default is "lambda.min").
return_fit: Logical. If TRUE, return the complete fit object.

References

The original source code is adapted from the sparsevar package, which is distributed under the GNU General Public License v2.