sparseVARMA {bigtime} | R Documentation |
Sparse Estimation of the Vector AutoRegressive Moving Average (VARMA) Model
sparseVARMA(Y, U = NULL, VARp = NULL, VARpen = "HLag", VARlseq = NULL, VARgran = NULL, VARalpha = 0, VARMAp = NULL, VARMAq = NULL, VARMApen = "HLag", VARMAlPhiseq = NULL, VARMAPhigran = NULL, VARMAlThetaseq = NULL, VARMAThetagran = NULL, VARMAalpha = 0, h = 1, cvcut = 0.9, eps = 10^-3)
Y |
A T by k matrix of time series. If k=1, a univariate autoregressive moving average model is estimated. |
U |
A T by k matrix of (approximated) error terms. Typical usage is to have the program estimate a high-order VAR model (Phase I) to get approximated error terms U. |
VARp |
User-specified maximum autoregressive lag order of the PhaseI 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 in PhaseI VAR. |
VARlseq |
User-specified grid of values for regularization parameter in the PhaseI VAR. 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 of the PhaseI VAR: 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 in PhaseI VAR. The default is zero. |
VARMAp |
User-specified maximum autoregressive lag order of the VARMA. Typical usage is to have the program compute its own maximum lag order based on the time series length. |
VARMAq |
User-specified maximum moving average lag order of the VARMA. Typical usage is to have the program compute its own maximum lag order based on the time series length. |
VARMApen |
"HLag" (hierarchical sparse penalty) or "L1" (standard lasso penalty) penalization in the VARMA. |
VARMAlPhiseq |
User-specified grid of values for regularization parameter corresponding to the autoregressive coefficients in the VARMA. Typical usage is to have the program compute its own grid. Supplying a grid of values overrides this. WARNING: use with care. |
VARMAPhigran |
User-specified vector of granularity specifications for the penalty parameter grid corresponding to the autoregressive coefficients in the VARMA: First element specifies how deep the grid should be constructed. Second element specifies how many values the grid should contain. |
VARMAlThetaseq |
User-specified grid of values for regularization parameter corresponding to the moving average coefficients in the VARMA. Typical usage is to have the program compute its own grid. Supplying a grid of values overrides this. WARNING: use with care. |
VARMAThetagran |
User-specified vector of granularity specifications for the penalty parameter grid corresponding to the moving average coefficients in the VARMA: First element specifies how deep the grid should be constructed. Second element specifies how many values the grid should contain. |
VARMAalpha |
a small positive regularization parameter value corresponding to squared Frobenius penalty in VARMA. The default is zero. |
h |
Desired forecast horizon in time-series cross-validation procedure. |
cvcut |
Proportion of observations used for model estimation in the time series cross-validation procedure. The remainder is used for forecast evaluation. |
eps |
a small positive numeric value giving the tolerance for convergence in the proximal gradient algorithms. |
A list with the following components
Y |
T by k matrix of time series. |
U |
Matrix of (approximated) error terms. |
k |
Number of time series. |
VARp |
Maximum autoregressive lag order of the PhaseI VAR. |
VARPhihat |
Matrix of estimated autoregressive coefficients of the Phase I VAR. |
VARphi0hat |
Vector of Phase I VAR intercepts. |
VARMAp |
Maximum autoregressive lag order of the VARMA. |
VARMAq |
Maximum moving average lag order of the VARMA. |
Phihat |
Matrix of estimated autoregressive coefficients of the VARMA. |
Thetahat |
Matrix of estimated moving average coefficients of the VARMA. |
phi0hat |
Vector of VARMA intercepts. |
Wilms Ines, Sumanta Basu, Bien Jacob and Matteson David S. (2017), "Sparse Identification and Estimation of High-Dimensional Vector AutoRegressive Moving Averages" arXiv preprint <arXiv:1707.09208>.
data(Y) VARMAfit <- sparseVARMA(Y) # sparse VARMA y <- matrix(Y[,1], ncol=1) ARMAfit <- sparseVARMA(y) # sparse ARMA