bvar_minnesota: Fitting Bayesian VAR(p) of Minnesota Prior

In bvhar: Bayesian Vector Heterogeneous Autoregressive Modeling

Fitting Bayesian VAR(p) of Minnesota Prior

Description

This function fits BVAR(p) with Minnesota prior.

Usage

bvar_minnesota(
  y,
  p = 1,
  num_chains = 1,
  num_iter = 1000,
  num_burn = floor(num_iter/2),
  thinning = 1,
  bayes_spec = set_bvar(),
  scale_variance = 0.05,
  include_mean = TRUE,
  parallel = list(),
  verbose = FALSE,
  num_thread = 1
)

## S3 method for class 'bvarmn'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

## S3 method for class 'bvarhm'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

## S3 method for class 'bvarmn'
logLik(object, ...)

## S3 method for class 'bvarmn'
AIC(object, ...)

## S3 method for class 'bvarmn'
BIC(object, ...)

is.bvarmn(x)

## S3 method for class 'bvarmn'
knit_print(x, ...)

## S3 method for class 'bvarhm'
knit_print(x, ...)

Arguments

y	Time series data of which columns indicate the variables
p	VAR lag (Default: 1)
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
bayes_spec	A BVAR model specification by set_bvar().
scale_variance	Proposal distribution scaling constant to adjust an acceptance rate
include_mean	Add constant term (Default: TRUE) or not (FALSE)
parallel	List the same argument of optimParallel::optimParallel(). By default, this is empty, and the function does not execute parallel computation.
verbose	Print the progress bar in the console. By default, FALSE.
num_thread	Number of threads
x	Any object
digits	digit option to print
...	not used
object	A bvarmn object

Details

Minnesota prior gives prior to parameters A (VAR matrices) and \Sigma_e (residual covariance).

A \mid \Sigma_e \sim MN(A_0, \Omega_0, \Sigma_e)

\Sigma_e \sim IW(S_0, \alpha_0)

(MN: matrix normal, IW: inverse-wishart)

Value

bvar_minnesota() returns an object bvarmn class. It is a list with the following components:

coefficients

Posterior Mean

fitted.values

Fitted values

residuals

Residuals

mn_mean

Posterior mean matrix of Matrix Normal distribution

mn_prec

Posterior precision matrix of Matrix Normal distribution

iw_scale

Posterior scale matrix of posterior inverse-Wishart distribution

iw_shape

Posterior shape of inverse-Wishart distribution (alpha_0 - obs + 2). \alpha_0: nrow(Dummy observation) - k

df

Numer of Coefficients: mp + 1 or mp

m

Dimension of the time series

obs

Sample size used when training = totobs - p

prior_mean

Prior mean matrix of Matrix Normal distribution: A_0

prior_precision

Prior precision matrix of Matrix Normal distribution: \Omega_0^{-1}

prior_scale

Prior scale matrix of inverse-Wishart distribution: S_0

prior_shape

Prior shape of inverse-Wishart distribution: \alpha_0

y0

Y_0

design

X_0

p

Lag of VAR

totobs

Total number of the observation

type

include constant term (const) or not (none)

y

Raw input (matrix)

call

Matched call

process

Process string in the bayes_spec: BVAR_Minnesota

spec

Model specification (bvharspec)

It is also normaliw and bvharmod class.

References

Bańbura, M., Giannone, D., & Reichlin, L. (2010). Large Bayesian vector auto regressions. Journal of Applied Econometrics, 25(1).

Giannone, D., Lenza, M., & Primiceri, G. E. (2015). Prior Selection for Vector Autoregressions. Review of Economics and Statistics, 97(2).

Litterman, R. B. (1986). Forecasting with Bayesian Vector Autoregressions: Five Years of Experience. Journal of Business & Economic Statistics, 4(1), 25.

KADIYALA, K.R. and KARLSSON, S. (1997), NUMERICAL METHODS FOR ESTIMATION AND INFERENCE IN BAYESIAN VAR-MODELS. J. Appl. Econ., 12: 99-132.

Karlsson, S. (2013). Chapter 15 Forecasting with Bayesian Vector Autoregression. Handbook of Economic Forecasting, 2, 791-897.

Sims, C. A., & Zha, T. (1998). Bayesian Methods for Dynamic Multivariate Models. International Economic Review, 39(4), 949-968.

See Also

• set_bvar() to specify the hyperparameters of Minnesota prior.

• summary.normaliw() to summarize BVAR model

Examples

# Perform the function using etf_vix dataset
fit <- bvar_minnesota(y = etf_vix[,1:3], p = 2)
class(fit)

# Extract coef, fitted values, and residuals
coef(fit)
head(residuals(fit))
head(fitted(fit))

bvhar documentation built on April 4, 2025, 5:22 a.m.