Forecast Error Variance Decomposition for Cholesky-Identified VARs

Computes the forecast error variance decomposition (FEVD) showing the proportion of forecast error variance of each variable attributable to each structural shock identified via Cholesky decomposition.

Usage

fevd_chol(chol_irf, shock = 0L)

Arguments

chol_irf: N x N x (horizon+1) cube of Cholesky impulse response functions from fcholeskyIRF. Each slice chol_irf[,,h] contains the responses at horizon h. The horizon is automatically inferred from the cube dimensions.
shock: Integer (1-indexed). If provided, returns only the N x horizon matrix for that specific shock (matching MATLAB variance_decomp(irf, shock)). If 0 (default), returns the full N x N x horizon cube for all shocks.

Value

A list containing:

fevd: If shock = 0: N x N x horizon cube where fevd[i,j,h] is the share of forecast error variance of variable i at horizon h explained by shock j. If shock > 0: N x horizon matrix for the specified shock.

Details

The forecast error variance decomposition measures the proportion of the h-step ahead forecast error variance of variable i that is attributable to each structural shock j. For Cholesky-identified VARs:

$$FEVD(i,j,h) = \frac{\sum_{s=0}^{h} [\Psi_s P]_{ij}^2}{\sum_{k=1}^{N} \sum_{s=0}^{h} [\Psi_s P]_{ik}^2}$$

Examples

if (FALSE) { # \dontrun{
# Estimate VAR
var_result <- fVAR(y, p = 2, c = 1)
wold <- fwoldIRF(var_result, horizon = 20)
S <- t(chol(var_result$sigma_full))
chol_irf <- fcholeskyIRF(wold, S)

# Full decomposition (all shocks) — returns 3D cube
vardec <- fevd_chol(chol_irf)

# Single shock decomposition — returns N x horizon matrix
shock <- match("UNCERT", colnames(y))
vardec <- fevd_chol(chol_irf, shock = shock)
} # }