Fitting Bayesian VAR(p) of Minnesota Prior

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: bvarhm object
digits: digit option to print
...: not used
object: A bvarmn object

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.

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)

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.

Examples