Compute Cholesky Impulse Response Functions

Usage

fcholeskyIRF(wold, S)

Arguments

wold: Wold representation cube (N x N x horizon)
S: Cholesky factor matrix (N x N), lower triangular

Value

A cube containing: Cholesky structural impulse response functions (N x N x horizon)

Details

This function computes structural impulse response functions using the Cholesky decomposition identification scheme. For each horizon h, the structural IRF is computed as: $$IRF_h = \Psi_h \cdot S$$ where $\Psi_h$ is the Wold representation at horizon h and S is the Cholesky factor (lower triangular) of the covariance matrix of reduced-form residuals.

The Cholesky identification imposes a recursive structure on the contemporaneous relationships between variables, with the ordering of variables determining the causal structure.

Examples

if (FALSE) { # \dontrun{
# Generate sample Wold representation
N <- 3
horizon <- 20
wold <- array(rnorm(N * N * horizon), dim = c(N, N, horizon))

# Compute Cholesky factor
Sigma <- matrix(c(1, 0.5, 0.3,
                  0.5, 1, 0.4,
                  0.3, 0.4, 1), 3, 3)
S <- t(chol(Sigma))  # Lower triangular

# Compute Cholesky IRF
chol_irf <- fcholeskyIRF(wold, S)
} # }