get_B_yt computes the impact matrix \(B_{y,t}\). For "ind_Student" and "ind_skewed_t" models
\(B_{y,t}=\sum_{m=1}^M\alpha_{m,t}B_m\). For models identified by heteroskedasticity \(B_{y,t}=W\sqrt{\sum_{m=1}^M\alpha_{m,t}\Lambda_m}\).
For recursive identification \(B_{y,t}\) is obtained from the Cholesky decomposition of the conditional covariance matrix.
get_B_yt(
all_Omegas,
alpha_mt,
W,
lambdas,
cond_dist = c("Gaussian", "Student", "ind_Student", "ind_skewed_t"),
identification = c("reduced_form", "recursive", "non-Gaussianity",
"heteroskedasticity")
)Returns the \((d \times d)\) impact matrix for the time period \(t\).
a 3D array such that the covariance matrix (or impact matrix \(B_m\)) of the \(m\)th regime is obtained from all_Omegas[, , m].
an \((M \times 1)\) vector containing the time period \(t\) transition weights.
a \((d \times d)\) matrix containing the matrix \(W\) for models identified by heteroskedasticity (as returned by pick_W).
a \((d(M-1)\times 1)\) vector \(\lambda_2,...,\lambda_M\) for models identified by heteroskedasticity (as returned by pick_lambdas).
specifies the conditional distribution of the model as "Gaussian", "Student", "ind_Student",
or "ind_skewed_t", where "ind_Student" the Student's \(t\) distribution with independent components, and
"ind_skewed_t" is the skewed \(t\) distribution with independent components (see Hansen, 1994).
is it reduced form model or an identified structural model; if the latter, how is it identified (see the vignette or the references for details)?
"reduced_form":Reduced form model.
"recursive":The usual lower-triangular recursive identification of the shocks via their impact responses.
"heteroskedasticity":Identification by conditional heteroskedasticity, which imposes constant relative impact responses for each shock.
"non-Gaussianity":Identification by non-Gaussianity; requires mutually independent non-Gaussian shocks, thus,
currently available only with the conditional distribution "ind_Student".
This is used in simulation of the counterfactual scenarios.