Fitting Bayesian VAR with Coefficient and Covariance Prior

This function fits BVAR. Covariance term can be homoskedastic or heteroskedastic (stochastic volatility). It can have Minnesota, SSVS, and Horseshoe prior.

Usage

var_bayes(
  y,
  p,
  exogen = NULL,
  s = 0,
  factor_spec = set_factor(),
  num_chains = 1,
  num_iter = 1000,
  num_burn = floor(num_iter/2),
  thinning = 1,
  coef_spec = set_bvar(),
  contem_spec = coef_spec,
  cov_spec = set_ldlt(),
  intercept = set_intercept(),
  exogen_spec = coef_spec,
  loading_spec = coef_spec,
  include_mean = TRUE,
  minnesota = TRUE,
  ggl = TRUE,
  save_init = FALSE,
  convergence = NULL,
  verbose = FALSE,
  num_thread = 1
)

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

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

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

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

Arguments

y

Time series data of which columns indicate the variables

p

VAR lag

exogen

Unmodeled variables

s

Lag of exogeneous variables in VARX(p, s). By default, s = 0.

factor_spec

Factor augmentation specification by set_factor().

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

coef_spec

Coefficient prior specification by set_bvar(), set_ssvs(), or set_horseshoe().

contem_spec

Contemporaneous coefficient prior specification by set_bvar(), set_ssvs(), or set_horseshoe().

cov_spec

SV specification by set_sv().

intercept

Prior for the constant term by set_intercept().

exogen_spec

Exogenous coefficient prior specification.

loading_spec

Factor loading prior specification.

include_mean

Add constant term (Default: TRUE) or not (FALSE)

minnesota

Apply cross-variable shrinkage structure (Minnesota-way). By default, TRUE.

ggl

If TRUE (default), use additional group shrinkage parameter for group structure. Otherwise, use group shrinkage parameter instead of global shirnkage parameter. Applies to HS, NG, and DL priors.

save_init

Save every record starting from the initial values (TRUE). By default, exclude the initial values in the record (FALSE), even when num_burn = 0 and thinning = 1. If num_burn > 0 or thinning != 1, this option is ignored.

convergence

Convergence threshold for rhat < convergence. By default, NULL which means no warning.

verbose

Print the progress bar in the console. By default, FALSE.

num_thread

Number of threads

x

bvarldlt object

digits

digit option to print

...

not used

Value

var_bayes() returns an object named bvarsv class.

coefficients

Posterior mean of coefficients.

chol_posterior

Posterior mean of contemporaneous effects.

param

Every set of MCMC trace.

param_names

Name of every parameter.

group

Indicators for group.

num_group

Number of groups.

df

Numer of Coefficients: 3m + 1 or 3m

p

VAR lag

m

Dimension of the data

obs

Sample size used when training = totobs - p

totobs

Total number of the observation

call

Matched call

process

Description of the model, e.g. VHAR_SSVS_SV, VHAR_Horseshoe_SV, or VHAR_minnesota-part_SV

type

include constant term (const) or not (none)

spec

Coefficients prior specification

sv

log volatility prior specification

intercept

Intercept prior specification

init

Initial values

chain

The numer of chains

iter

Total iterations

burn

Burn-in

thin

Thinning

y0

\(Y_0\)

design

\(X_0\)

y

Raw input

If it is SSVS or Horseshoe:

pip

Posterior inclusion probabilities.

Details

Cholesky stochastic volatility modeling for VAR based on $$\Sigma_t^{-1} = L^T D_t^{-1} L$$, and implements corrected triangular algorithm for Gibbs sampler.

References

Carriero, A., Chan, J., Clark, T. E., & Marcellino, M. (2022). Corrigendum to “Large Bayesian vector autoregressions with stochastic volatility and non-conjugate priors” [J. Econometrics 212 (1)(2019) 137-154]. Journal of Econometrics, 227(2), 506-512.

Chan, J., Koop, G., Poirier, D., & Tobias, J. (2019). Bayesian Econometric Methods (2nd ed., Econometric Exercises). Cambridge: Cambridge University Press.

Cogley, T., & Sargent, T. J. (2005). Drifts and volatilities: monetary policies and outcomes in the post WWII US. Review of Economic Dynamics, 8(2), 262-302.

Gruber, L., & Kastner, G. (2022). Forecasting macroeconomic data with Bayesian VARs: Sparse or dense? It depends! arXiv.

Huber, F., Koop, G., & Onorante, L. (2021). Inducing Sparsity and Shrinkage in Time-Varying Parameter Models. Journal of Business & Economic Statistics, 39(3), 669-683.

Korobilis, D. (2022). A new algorithm for structural restrictions in Bayesian vector autoregressions. European Economic Review, 148, 104241.

Korobilis, D., & Shimizu, K. (2022). Bayesian Approaches to Shrinkage and Sparse Estimation. Foundations and Trends® in Econometrics, 11(4), 230-354.

Ray, P., & Bhattacharya, A. (2018). Signal Adaptive Variable Selector for the Horseshoe Prior. arXiv.