post_gamma_measurement_variance: Posterior Draws of Error Variances

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

Posterior Draws of Error Variances

Description

Produces a draw of the constant diagonal error variance matrix of the measurement equation of a state space model using an inverse gamma posterior density.

Usage

post_gamma_measurement_variance(u, shape_prior, rate_prior, inverse)

Arguments

u	a KT \times 1 vector of errors.
shape_prior	a K \times 1 vector of prior shape parameters.
rate_prior	a K \times 1 vector of prior rate parameters.
inverse	logical. If TRUE, the function returns the precision matrix, i.e. the inverse of the variance matrix. Defaults to FALSE.

Details

For a model with measurement equation

y_t = Z_{t} a_t + u_t

with u_t \sim N(0, \Sigma_{u}) the function produces a draw of the constant diagonal error variance matrix \Simga_u.

Value

A matrix.

References

Chan, J., Koop, G., Poirier, D. J., & Tobias J. L. (2019). Bayesian econometric methods (2nd ed.). Cambridge: Cambridge University Press.

Examples

k <- 10 # Number of endogenous variables
tt <- 1000 # Number of observations

set.seed(1234) # Set RNG seed

# Generate artificial error series with N(0, 1)
u <- matrix(rnorm(k * tt))

# Define priors
shape_prior <- matrix(1, k)
rate_prior <- matrix(.0001, k)

# Obtain posterior draw
post_gamma_measurement_variance(u, shape_prior, rate_prior, inverse = FALSE)

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