summary.normaliw: Summarizing Bayesian Multivariate Time Series Model
In bvhar: Bayesian Vector Heterogeneous Autoregressive Modeling

summary.normaliw

R Documentation

Summarizing Bayesian Multivariate Time Series Model

Description

summary 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 `normaliw` object
`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.normaliw` object
`digits`	digit option to print

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.

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

References

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).

bvhar documentation built on June 25, 2025, 9:07 a.m.