summary method for normaliw class.
# S3 method for normaliw
summary(
object,
num_chains = 1,
num_iter = 1000,
num_burn = floor(num_iter/2),
thinning = 1,
verbose = FALSE,
num_thread = 1,
...
)# S3 method for summary.normaliw
print(x, digits = max(3L, getOption("digits") - 3L), ...)
# S3 method for summary.normaliw
knit_print(x, ...)
summary.normaliw
class has the following components:
Variable names
Total number of the observation
Sample size used when training = totobs - p
Lag of VAR
Dimension of the data
Matched call
Model specification (bvharspec)
MN Mean of posterior distribution (MN-IW)
MN Precision of posterior distribution (MN-IW)
IW scale of posterior distribution (MN-IW)
IW df of posterior distribution (MN-IW)
Number of MCMC iterations
Number of MCMC burn-in
MCMC thinning
MCMC record of coefficients vector
MCMC record of upper cholesky factor
MCMC record of diagonal of cholesky factor
MCMC record of upper part of cholesky factor
MCMC record of every parameter
Posterior mean of coefficients
Posterior mean of covariance
A normaliw object
Number of MCMC chains
MCMC iteration number
Number of burn-in (warm-up). Half of the iteration is the default choice.
Thinning every thinning-th iteration
Print the progress bar in the console. By default, FALSE.
Number of threads
not used
summary.normaliw object
digit option to print
From Minnesota prior, set of coefficient matrices and residual covariance matrix have matrix Normal Inverse-Wishart distribution.
BVAR:
$$(A, \Sigma_e) \sim MNIW(\hat{A}, \hat{V}^{-1}, \hat\Sigma_e, \alpha_0 + n)$$ where \(\hat{V} = X_\ast^T X_\ast\) is the posterior precision of MN.
BVHAR:
$$(\Phi, \Sigma_e) \sim MNIW(\hat\Phi, \hat{V}_H^{-1}, \hat\Sigma_e, \nu + n)$$ where \(\hat{V}_H = X_{+}^T X_{+}\) is the posterior precision of MN.
Litterman, R. B. (1986). Forecasting with Bayesian Vector Autoregressions: Five Years of Experience. Journal of Business & Economic Statistics, 4(1), 25.
Bańbura, M., Giannone, D., & Reichlin, L. (2010). Large Bayesian vector auto regressions. Journal of Applied Econometrics, 25(1).