sparseVAR: Sparse Estimation of the Vector AutoRegressive (VAR) Model

Description

Sparse Estimation of the Vector AutoRegressive (VAR) Model

Usage

sparseVAR(
  Y,
  p = NULL,
  VARpen = "HLag",
  VARlseq = NULL,
  VARgran = NULL,
  selection = c("none", "cv", "bic", "aic", "hq"),
  cvcut = 0.9,
  h = 1,
  eps = 0.001,
  check_std = TRUE,
  verbose = FALSE
)

Value

A list with the following components

Y: \(T\) by \(k\) matrix of time series.
k: Number of time series.
p: Maximum autoregressive lag order of the VAR.
Phihat: Matrix of estimated autoregressive coefficients of the VAR.
phi0hat: vector of VAR intercepts.
series_names: names of time series
lambdas: sparsity parameter grid
MSFEcv: MSFE cross-validation scores for each value of the sparsity parameter in the considered grid
MSFEcv_all: MSFE cross-validation full output
lambda_opt: Optimal value of the sparsity parameter as selected by the time-series cross-validation procedure
lambda_SEopt: Optimal value of the sparsity parameter as selected by the time-series cross-validation procedure and after applying the one-standard-error rule. This is the value used.
h: Forecast horizon h

Arguments

Y: A \(T\) by \(k\) matrix of time series. If k=1, a univariate autoregressive model is estimated.
p: User-specified maximum autoregressive lag order of the VAR. Typical usage is to have the program compute its own maximum lag order based on the time series length.
VARpen: "HLag" (hierarchical sparse penalty) or "L1" (standard lasso penalty) penalization.
VARlseq: User-specified grid of values for regularization parameter corresponding to sparse penalty. Typical usage is to have the program compute its own grid. Supplying a grid of values overrides this. WARNING: use with care.
VARgran: User-specified vector of granularity specifications for the penalty parameter grid: First element specifies how deep the grid should be constructed. Second element specifies how many values the grid should contain.
selection: One of "none" (default), "cv" (Time Series Cross-Validation), "bic", "aic", "hq". Used to select the optimal penalization.
cvcut: Proportion of observations used for model estimation in the time series cross-validation procedure. The remainder is used for forecast evaluation. Redundant if selection is not "cv".
h: Desired forecast horizon in time-series cross-validation procedure.
eps: a small positive numeric value giving the tolerance for convergence in the proximal gradient algorithm.
check_std: Check whether data is standardised. Default is TRUE and is not recommended to be changed
verbose: Logical to print value of information criteria for each lambda together with selection. Default is FALSE

References

Nicholson William B., Wilms Ines, Bien Jacob and Matteson David S. (2020), “High-dimensional forecasting via interpretable vector autoregression”, Journal of Machine Learning Research, 21(166), 1-52.

Examples

Run this code

data(var.example)
VARfit <- sparseVAR(Y = scale(Y.var)) # sparse VAR
ARfit <- sparseVAR(Y=scale(Y.var[,2])) # sparse AR