unWvec forms a square matrix from a vector of
stacked columns where zeros are removed according to structural
parameter constaints.
unWvec(Wvector, d, structural_pars = NULL)a \((d x d)\) matrix \(W\).
a length \(d^2 - n_zeros\) vector where \(n_zeros\) is the
number of zero entries in the matrix W.
the number of rows in the square matrix to be formed.
If NULL a reduced form model is considered. Reduced models can be used directly as recursively
identified structural models. For a structural model identified by conditional heteroskedasticity, should be a list containing
at least the first one of the following elements:
W - a \((dxd)\) matrix with its entries imposing constraints on \(W\): NA indicating that the element is
unconstrained, a positive value indicating strict positive sign constraint, a negative value indicating strict
negative sign constraint, and zero indicating that the element is constrained to zero.
C_lambda - a \((d(M-1) x r)\) constraint matrix that satisfies (\(\lambda\)\(_{2}\)\(,...,\)
\(\lambda\)\(_{M}) =\) \(C_{\lambda} \gamma\) where \(\gamma\) is the new \((r x 1)\)
parameter subject to which the model is estimated (similarly to AR parameter constraints). The entries of C_lambda
must be either positive or zero. Ignore (or set to NULL) if the eigenvalues \(\lambda_{mi}\)
should not be constrained.
fixed_lambdas - a length \(d(M-1)\) numeric vector (\(\lambda\)\(_{2}\)\(,...,\)
\(\lambda\)\(_{M})\) with elements strictly larger than zero specifying the fixed parameter values for the
parameters \(\lambda_{mi}\) should be constrained to. This constraint is alternative C_lambda.
Ignore (or set to NULL) if the eigenvalues \(\lambda_{mi}\) should not be constrained.
See Virolainen (forthcoming) for the conditions required to identify the shocks and for the B-matrix as well (it is \(W\) times a time-varying diagonal matrix with positive diagonal entries).
No argument checks!