get_B_yt: Compute the impact matrix B_{y,t} for a single time period

In sstvars: Toolkit for Reduced Form and Structural Smooth Transition Vector Autoregressive Models

Compute the impact matrix B_{y,t} for a single time period

Description

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.

Usage

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")
)

Arguments

all_Omegas	a 3D array such that the covariance matrix (or impact matrix B_m) of the mth regime is obtained from all_Omegas[, , m].
alpha_mt	an (M \times 1) vector containing the time period t transition weights.
W	a (d \times d) matrix containing the matrix W for models identified by heteroskedasticity (as returned by pick_W).
lambdas	a (d(M-1)\times 1) vector \lambda_2,...,\lambda_M for models identified by heteroskedasticity (as returned by pick_lambdas).
cond_dist	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).
identification	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".

Details

This is used in simulation of the counterfactual scenarios.

Value

Returns the (d \times d) impact matrix for the time period t.

sstvars documentation built on Sept. 16, 2025, 1:09 a.m.