Description Usage Arguments Value See Also Examples
Sparse Estimation of the Vector AutoRegressive with Exogenous Variables X (VARX) Model
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Y |
A T by k matrix of time series. If k=1, a univariate autoregressive model is estimated. |
X |
A T by m matrix of time series. |
p |
User-specified maximum endogenous autoregressive lag order. Typical usage is to have the program compute its own maximum lag order based on the time series length. |
s |
User-specified maximum exogenous autoregressive lag order. Typical usage is to have the program compute its own maximum lag order based on the time series length. |
VARXpen |
"HLag" (hierarchical sparse penalty) or "L1" (standard lasso penalty) penalization in VARX. |
VARXlPhiseq |
User-specified grid of values for regularization parameter corresponding to the endogenous autoregressive coefficients in the VARX. Typical usage is to have the program compute its own grid. Supplying a grid of values overrides this. WARNING: use with care. |
VARXPhigran |
User-specified vector of granularity specifications for the penalty parameter grid corresponding to the endogenous autoregressive coefficients in the VARX: First element specifies how deep the grid should be constructed. Second element specifies how many values the grid should contain. |
VARXlBseq |
User-specified grid of values for regularization parameter corresponding to the exogenous autoregressive coefficients in the VARX. Typical usage is to have the program compute its own grid. Supplying a grid of values overrides this. WARNING: use with care. |
VARXBgran |
User-specified vector of granularity specifications for the penalty parameter grid corresponding to the exogenous autoregressive coefficients in the VARX: First element specifies how deep the grid should be constructed. Second element specifies how many values the grid should contain. |
VARXalpha |
a small positive regularization parameter value corresponding to squared Frobenius penalty. 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 algorithm. |
A list with the following components
Y |
T by k matrix of endogenous time series. |
X |
T by m matrix of exogenous time series. |
k |
Number of endogenous time series. |
m |
Number of exogenous time series. |
p |
Maximum endogenous autoregressive lag order of the VARX. |
s |
Maximum exogenouss autoregressive lag order of the VARX. |
Phihat |
Matrix of estimated endogenous autoregressive coefficients. |
Bhat |
Matrix of estimated exogenous autoregressive coefficients. |
phi0hat |
vector of VARX intercepts. |
exogenous_series_names |
names of the exogenous time series |
endogenous_series_names |
names of the endogenous time series |
lambdaPhi |
sparsity parameter grid corresponding to endogenous autoregressive parameters |
lambdaB |
sparsity parameter grid corresponding to exogenous autoregressive parameters |
lambdaPhi_opt |
Optimal value of the sparsity parameter (corresponding to the endogenous autoregressive parameters) as selected by the time-series cross-validation procedure |
lambdaPhi_SEopt |
Optimal value of the sparsity parameter (corresponding to the endogenous autoregressive parameters) as selected by the time-series cross-validation procedure and after applying the one-standard-error rule |
lambdaB_opt |
Optimal value of the sparsity parameter (corresponding to the exogenous autoregressive parameters) as selected by the time-series cross-validation procedure |
lambdaB_SEopt |
Optimal value of the sparsity parameter (corresponding to the exogenous autoregressive parameters) as selected by the time-series cross-validation procedure and after applying the one-standard-error rule |
MSFEcv |
MSFE cross-validation scores for each value in the two-dimensional sparsity grid |
h |
Forecast horizon h |
lagmatrix and directforecast
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