summary.normaliw {bvhar}

Summarizing Bayesian Multivariate Time Series Model

Description

summary method for normaliw class.

Usage

## S3 method for class 'normaliw'
summary(
  object,
  num_iter = 10000L,
  num_burn = floor(num_iter/2),
  thinning = 1L,
  ...
)

## 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

normaliw object

num_iter

Number to sample MNIW distribution

num_burn

Number of burn-in

thinning

Thinning every thinning-th iteration

...

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).