var_bayes: Fitting Bayesian VAR with Coefficient and Covariance Prior

Description

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,
  num_chains = 1,
  num_iter = 1000,
  num_burn = floor(num_iter/2),
  thinning = 1,
  bayes_spec = set_bvar(),
  cov_spec = set_ldlt(),
  intercept = set_intercept(),
  include_mean = TRUE,
  minnesota = TRUE,
  ggl = TRUE,
  save_init = FALSE,
  convergence = NULL,
  verbose = FALSE,
  num_thread = 1
)
# S3 method for bvarsv
print(x, digits = max(3L, getOption("digits") - 3L), ...)
# S3 method for bvarldlt
print(x, digits = max(3L, getOption("digits") - 3L), ...)
# S3 method for bvarsv
knit_print(x, ...)
# S3 method for bvarldlt
knit_print(x, ...)

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.

Arguments

y: Time series data of which columns indicate the variables
p: VAR lag
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(), set_ssvs(), or set_horseshoe().
cov_spec: SV specification by set_sv().
intercept: Prior for the constant term by set_intercept().
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

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., & 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.