Fitting Bayesian VAR-SV — bvar

This function fits VAR-SV. It can have Minnesota, SSVS, and Horseshoe prior.

Usage

bvar_sv(
  y,
  p,
  num_chains = 1,
  num_iter = 1000,
  num_burn = floor(num_iter/2),
  thinning = 1,
  bayes_spec = set_bvar(),
  sv_spec = set_sv(),
  intercept = set_intercept(),
  include_mean = TRUE,
  minnesota = TRUE,
  save_init = FALSE,
  verbose = FALSE,
  num_thread = 1
)

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

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

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().
sv_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.
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.
verbose: Print the progress bar in the console. By default, FALSE.
num_thread: Number of threads
x: bvarsv object
digits: digit option to print
...: not used

Value

bvar_sv() returns an object named bvarsv

class.

alpha_record: MCMC trace for vectorized coefficients ($\alpha$) with posterior::draws_df format.
h_record: MCMC trace for log-volatilities.
a_record: MCMC trace for contemporaneous coefficients.
h0_record: MCMC trace for initial log-volatilities.
sigh_record: MCMC trace for log-volatilities variance.
coefficients: Posterior mean of coefficients.
chol_posterior: Posterior mean of contemporaneous effects.
pip: Posterior inclusion probabilities.
param: Every set of MCMC trace.
group: Indicators for group.
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"} \item{type}{include constant term ("const") or not ("none"`)
spec: Coefficients prior specification
sv: log volatility prior specification
chain: The numer of chains
iter: Total iterations
burn: Burn-in
thin: Thinning
y0: $Y_0$
design: $X_0$
y: Raw input

Different members are added according to priors. If it is SSVS:

gamma_record: MCMC trace for dummy variable.

Horseshoe:

lambda_record: MCMC trace for local shrinkage level.
tau_record: MCMC trace for global shrinkage level.
kappa_record: MCMC trace for shrinkage factor.

Details

Cholesky stochastic volatility modeling for VAR based on $$\Sigma_t = L^T D_t^{-1} L$$

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.