post_normal_covar_tvp {bvartools}

Posterior Simulation of Error Covariance Coefficients

Description

Produces posterior draws of time varying error covariance coefficients.

Usage

post_normal_covar_tvp(y, u_omega_i, v_sigma_i, psi_init)

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.

v_sigma_i

matrix of error variances of the state equation. Either an M \times M matrix for constant variances or an MT \times MT matrix for time varying variances, where M is the number of estimated variables.

psi_init

a vector of inital values of the state equation.

Details

For the multivariate model A_{0,t} 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,t} similar as in Primiceri (2005), i.e., using

y_t = Z_t \psi_t + 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.

The algorithm of Chan and Jeliazkov (2009) is used to obtain time varying coefficients.

Value

A matrix.

References

Chan, J., & Jeliazkov, I. (2009). Efficient simulation and integrated likelihood estimation in state space models. International Journal of Mathematical Modelling and Numerical Optimisation, 1(1/2), 101–120. doi:10.1504/IJMMNO.2009.030090

Primiceri, G. E. (2005). Time varying structural vector autoregressions and monetary policy. The Review of Economic Studies, 72(3), 821–852. doi:10.1111/j.1467-937X.2005.00353.x

Examples

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

# Generate artificial draws of other matrices
u_omega_i <- diag(1, 3)
v_sigma_i <- diag(1000, 3)
psi_init <- matrix(0, 3)

# Obtain posterior draw
post_normal_covar_tvp(y, u_omega_i, v_sigma_i, psi_init)