sparseVAR {bigtime} | R Documentation |
Sparse Estimation of the Vector AutoRegressive (VAR) Model
sparseVAR(Y, p = NULL, VARpen = "HLag", VARlseq = NULL, VARgran = NULL, VARalpha = 0, cvcut = 0.9, h = 1, eps = 0.001)
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. |
VARalpha |
a small positive regularization parameter value corresponding to squared Frobenius penalty. The default is zero. |
cvcut |
Proportion of observations used for model estimation in the time series cross-validation procedure. The remainder is used for forecast evaluation. |
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. |
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. |
Nicholson William B., Bien Jacob and Matteson David S. (2017), "High Dimensional Forecasting via Interpretable Vector Autoregression" arXiv preprint <arXiv:1412.5250v2>.
data(Y) VARfit <- sparseVAR(Y) # sparse VAR y <- matrix(Y[,1], ncol=1) ARfit <- sparseVAR(y) # sparse AR