sparseVARMA {bigtime}  R Documentation 
Sparse Estimation of the Vector AutoRegressive Moving Average (VARMA) Model
Description
Sparse Estimation of the Vector AutoRegressive Moving Average (VARMA) Model
Usage
sparseVARMA(
Y,
U = NULL,
VARp = NULL,
VARpen = "HLag",
VARlseq = NULL,
VARgran = NULL,
VARselection = c("cv", "bic", "aic", "hq"),
VARMAp = NULL,
VARMAq = NULL,
VARMApen = "HLag",
VARMAlPhiseq = NULL,
VARMAPhigran = NULL,
VARMAlThetaseq = NULL,
VARMAThetagran = NULL,
VARMAalpha = 0,
VARMAselection = c("none", "cv", "bic", "aic", "hq"),
h = 1,
cvcut = 0.9,
eps = 10^3,
check_std = TRUE
)
Arguments
Y 
A 
U 
A 
VARp 
Userspecified 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 
Userspecified 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 
Userspecified 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. 
VARselection 
Selection procedure for the first stage. Default is time series CrossValidation. Alternatives are BIC, AIC, HQ 
VARMAp 
Userspecified 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 
Userspecified 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 
Userspecified 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 
Userspecified 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 
Userspecified 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 
Userspecified 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. 
VARMAselection 
selection procedure in the second stage. Default is "none"; Alternatives are cv, bic, aic, hq 
h 
Desired forecast horizon in timeseries crossvalidation procedure. 
cvcut 
Proportion of observations used for model estimation in the time series crossvalidation procedure. The remainder is used for forecast evaluation. 
eps 
a small positive numeric value giving the tolerance for convergence in the proximal gradient algorithms. 
check_std 
Check whether data is standardised. Default is TRUE and is not recommended to be changed 
Value
A list with the following components
Y 

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. 
series_names 
names of time series 
PhaseI_lambas 
Phase I sparsity parameter grid 
PhaseI_MSFEcv 
MSFE crossvalidation scores for each value of the sparsity parameter in the considered grid 
PhaseI_lambda_opt 
Phase I Optimal value of the sparsity parameter as selected by the timeseries crossvalidation procedure 
PhaseI_lambda_SEopt 
Phase I Optimal value of the sparsity parameter as selected by the timeseries crossvalidation procedure and after applying the onestandarderror rule 
PhaseII_lambdaPhi 
Phase II sparsity parameter grid corresponding to Phi parameters 
PhaseII_lambdaTheta 
Phase II sparsity parameter grid corresponding to Theta parameters 
PhaseII_lambdaPhi_opt 
Phase II Optimal value of the sparsity parameter (corresponding to Phi parameters) as selected by the timeseries crossvalidation procedure 
PhaseII_lambdaPhi_SEopt 
Phase II Optimal value of the sparsity parameter (corresponding to Theta parameters) as selected by the timeseries crossvalidation procedure and after applying the onestandarderror rule 
PhaseII_lambdaTheta_opt 
Phase II Optimal value of the sparsity parameter (corresponding to Phi parameters) as selected by the timeseries crossvalidation procedure 
PhaseII_lambdaTheta_SEopt 
Phase II Optimal value of the sparsity parameter (corresponding to Theta parameters) as selected by the timeseries crossvalidation procedure and after applying the onestandarderror rule 
PhaseII_MSFEcv 
Phase II MSFE crossvalidation scores for each value in the twodimensional sparsity grid 
h 
Forecast horizon h 
References
Wilms Ines, Sumanta Basu, Bien Jacob and Matteson David S. (2021), “Sparse Identification and Estimation of LargeScale Vector AutoRegressive Moving Averages”, Journal of the American Statistical Association, doi: 10.1080/01621459.2021.1942013.
See Also
Examples
data(varma.example)
VARMAfit < sparseVARMA(Y = scale(Y.varma)) # sparse VARMA
y < matrix(Y.varma[,1], ncol=1)
ARMAfit < sparseVARMA(Y=scale(y)) # sparse ARMA