Convert a matrix of VAR coefficients estimated by a shrinkage method into a list of "shrinklm" object, where the class "shrinklm" inherits the class "lm".
convPsi2varresult(
Psi,
Y,
X,
lambda0,
type = c("const", "trend", "both", "none"),
ybar = NULL,
xbar = NULL,
Q_values = NULL,
callstr = ""
)A list object with objects of class c("shrinklm", "lm"). Each "shrinklm" object has components: coefficients, residuals, fitted.values, rank, df.residual, lambda0, call, terms, svd
An M-by-K matrix of VAR coefficients
An N-by-K data matrix of dependent variables
An N-by-M data matrix of regressors
A rescaled shrinkage intensity parameter, based on which the effective number of parameters is computed by $$Trace(X(X'X + \lambda_0*I)^{-1} X')$$
Type of deterministic variables in the VAR estimation problem. Either of "const", "trend", "both", or "none".
NULL if Y and X are not centered. Mean vectors if Y and X had been centered. If Y and X had been centered (ybar and xbar are not NULL) and type is "const" or "both", then the coefficients for the constant term is computed and concatenated to the coefficients.
Nonnegative weight vector of length N. Default is NULL. Take weights on rows (samples) of Y and X by sqrt(Q).
The call to VARshrink().
Consider VAR(p) model: $$y_t = A_1 y_{t-1} + ... + A_p y_{t-p} + C d_t + e_t.$$ It can be written in the matrix form: $$Y = X \Psi + E,$$ where \(\Psi\) is a concatenated M-by-K matrix, \(\Psi = (A_1, ..., A_p, C)^T\). It can be written in the multiple linear regression form of a VAR(p) model: $$y_j = X \psi_j + e_j, \quad j=1,...,K,$$ where \(y_j\), \(\psi_j\), and \(e_j\) are the j-th column vectors of Y, \(\Psi\), and E, respectively. This function converts \(\Psi\) into a list of "shrinklm" objects, where each "shrinklm" object contains the length-M vector \(\psi_j\) as coefficients.
Considering that each coefficient vector \(\psi_j\) is estimated by a shrinkage method, the effective number of parameters, \(k_{eff}\), is computed as: $$k_{eff} = Trace(X (X^T X + \lambda_0 * I)^{-1} X^T).$$ Then, the degree of freedom of residuals is computed as: $$df.residual = N - k_{eff},$$ where N is the number of rows of data matrices Y and X.