sparsevarma: Sparse Estimation of the Vector AutoRegressive Moving Average...

In YiHou98/bigtime: Sparse Estimation of Large Time Series Models

Description

Sparse Estimation of the Vector AutoRegressive Moving Average (VARMA) Model

Usage

sparseVARMA(
  Y,
  U = NULL,
  VARp = NULL,
  VARpen = "HLag",
  VARlseq = NULL,
  VARgran = NULL,
  VARMAp = NULL,
  VARMAq = NULL,
  VARMApen = "HLag",
  VARMAlPhiseq = NULL,
  VARMAPhigran = NULL,
  VARMAlThetaseq = NULL,
  VARMAThetagran = NULL,
  VARMAalpha = 0,
  h = 1,
  cvcut = 0.9,
  eps = 10^-3
)

Arguments

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.
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.

Value

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.
series_names	names of time series
PhaseI_lambas	Phase I sparsity parameter grid
PhaseI_MSFEcv	MSFE cross-validation 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 time-series cross-validation procedure
PhaseI_lambda_SEopt	Phase I Optimal value of the sparsity parameter as selected by the time-series cross-validation procedure and after applying the one-standard-error 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 time-series cross-validation procedure
PhaseII_lambdaPhi_SEopt	Phase II Optimal value of the sparsity parameter (corresponding to Theta parameters) as selected by the time-series cross-validation procedure and after applying the one-standard-error rule
PhaseII_lambdaTheta_opt	Phase II Optimal value of the sparsity parameter (corresponding to Phi parameters) as selected by the time-series cross-validation procedure
PhaseII_lambdaTheta_SEopt	Phase II Optimal value of the sparsity parameter (corresponding to Theta parameters) as selected by the time-series cross-validation procedure and after applying the one-standard-error rule
PhaseII_MSFEcv	Phase II MSFE cross-validation scores for each value in the two-dimensional sparsity grid
h	Forecast horizon h

References

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>.

See Also

lagmatrix and directforecast

Examples

data(Y)
VARMAfit <- sparseVARMA(Y) # sparse VARMA
y <- matrix(Y[,1], ncol=1)
ARMAfit <- sparseVARMA(y) # sparse ARMA

YiHou98/bigtime documentation built on Dec. 18, 2021, 7:26 p.m.