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 June 8, 2025, 10:07 a.m.