Summarizing Bayesian Multivariate Time Series Model
Source:R/summary-bayes.R, R/print-summarymniw.R
summary.normaliw.Rdsummary method for normaliw class.
Usage
# S3 method for class '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 class 'summary.normaliw'
print(x, digits = max(3L, getOption("digits") - 3L), ...)
# S3 method for class 'summary.normaliw'
knit_print(x, ...)Arguments
- object
A
normaliwobject- num_chains
Number of MCMC chains
- num_iter
MCMC iteration number
- num_burn
Number of burn-in (warm-up). Half of the iteration is the default choice.
- thinning
Thinning every thinning-th iteration
- verbose
Print the progress bar in the console. By default,
FALSE.- num_thread
Number of threads
- ...
not used
- x
summary.normaliwobject- digits
digit option to print
Value
summary.normaliw class has the following components:
- names
Variable names
- totobs
Total number of the observation
- obs
Sample size used when training =
totobs-p- p
Lag of VAR
- m
Dimension of the data
- call
Matched call
- spec
Model specification (
bvharspec)- mn_mean
MN Mean of posterior distribution (MN-IW)
- mn_prec
MN Precision of posterior distribution (MN-IW)
- iw_scale
IW scale of posterior distribution (MN-IW)
- iw_shape
IW df of posterior distribution (MN-IW)
- iter
Number of MCMC iterations
- burn
Number of MCMC burn-in
- thin
MCMC thinning
- alpha_record (BVAR) and phi_record (BVHAR)
MCMC record of coefficients vector
- psi_record
MCMC record of upper cholesky factor
- omega_record
MCMC record of diagonal of cholesky factor
- eta_record
MCMC record of upper part of cholesky factor
- param
MCMC record of every parameter
- coefficients
Posterior mean of coefficients
- covmat
Posterior mean of covariance
Details
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.