bvar_sv {bvhar}

Fitting Bayesian VAR-SV

Description

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

## S3 method for class '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

Details

Cholesky stochastic volatility modeling for VAR based on

\Sigma_t = L^T D_t^{-1} L

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.

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.