post_normal_covar_const: Posterior Simulation of Error Covariance Coefficients

In franzmohr/bvartools: Bayesian Inference of Vector Autoregressive and Error Correction Models

Posterior Simulation of Error Covariance Coefficients

Description

Produces posterior draws of constant error covariance coefficients.

Usage

post_normal_covar_const(y, u_omega_i, k, prior_mean, prior_covariance_i)

Arguments

y	a K \times T matrix of data with K as the number of endogenous variables and T the number of observations.
u_omega_i	matrix of error variances of the measurement equation. Either a K \times K matrix for constant variances or a KT \times KT matrix for time varying variances.
k	number of endogenous variables.
prior_mean	vector of prior means. In case of TVP, this vector is used as initial condition.
prior_covariance_i	inverse prior covariance matrix. In case of TVP, this matrix is used as initial condition.

Details

For the multivariate model A_0 y_t = u_t with u_t \sim N(0, \Omega_t) the function produces a draw of the lower triangular part of A_0 similar as in Primiceri (2005), i.e., using

y_t = Z_t \psi + u_t,

where

Z_{t} = \begin{bmatrix} 0 & \dotsm & \dotsm & 0 \\ -y_{1, t} & 0 & \dotsm & 0 \\ 0 & -y_{[1,2], t} & \ddots & \vdots \\ \vdots & \ddots & \ddots & 0 \\ 0 & \dotsm & 0 & -y_{[1,...,K-1], t} \end{bmatrix}

and y_{[1,...,K-1], t} denotes the first to (K-1)th elements of the vector y_t.

Value

A matrix.

References

Primiceri, G. E. (2005). Time varying structural vector autoregressions and monetary policy. The Review of Economic Studies, 72(3), 821–852. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/j.1467-937X.2005.00353.x")}

Examples

# Load example data
data("e1")
y <- log(t(e1))
k <- nrow(y)
y <- matrix(y)

# Generate artificial draws of other matrices
u_omega_i <- Matrix(diag(1, k))
prior_mean <- matrix(0, 3)
prior_covariance_i <- Matrix(diag(0, 3))

# Obtain posterior draw
post_normal_covar_const(y, u_omega_i, k, prior_mean, prior_covariance_i)

franzmohr/bvartools documentation built on Jan. 28, 2024, 4:06 a.m.