bvar_ssvs: Fitting Bayesian VAR(p) of SSVS Prior

Description

This function fits BVAR(p) with stochastic search variable selection (SSVS) prior.

Usage

bvar_ssvs(
  y,
  p,
  num_chains = 1,
  num_iter = 1000,
  num_burn = floor(num_iter/2),
  thinning = 1,
  bayes_spec = choose_ssvs(y = y, ord = p, type = "VAR", param = c(0.1, 10), include_mean
    = include_mean, gamma_param = c(0.01, 0.01), mean_non = 0, sd_non = 0.1),
  init_spec = init_ssvs(type = "auto"),
  include_mean = TRUE,
  minnesota = FALSE,
  verbose = FALSE,
  num_thread = 1
)
# S3 method for bvarssvs
print(x, digits = max(3L, getOption("digits") - 3L), ...)
# S3 method for bvarssvs
knit_print(x, ...)

Value

bvar_ssvs returns an object named bvarssvs

class. It is a list with the following components:

coefficients: Posterior mean of VAR coefficients.

chol_posterior

Posterior mean of cholesky factor matrix

covmat

Posterior mean of covariance matrix

omega_posterior

Posterior mean of omega

pip

Posterior inclusion probability

param

posterior::draws_df with every variable: alpha, eta, psi, omega, and gamma

param_names

Name of every parameter.

Numer of Coefficients: mp + 1 or mp

Lag of VAR

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. VAR_SSVS

type

include constant term (const) or not (none)

spec

SSVS specification defined by set_ssvs()

init

Initial specification defined by init_ssvs()

chain

The numer of chains

iter

Total iterations

burn

Burn-in

thin

Thinning

group

Indicators for group.

num_group

Number of groups.

$Y_0$

design

$X_0$

Raw input

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 SSVS model specification by set_ssvs(). By default, use a default semiautomatic approach choose_ssvs().
init_spec: SSVS initialization specification by init_ssvs(). By default, use OLS for coefficient and cholesky factor while 1 for dummies.
include_mean: Add constant term (Default: TRUE) or not (FALSE)
minnesota: Apply cross-variable shrinkage structure (Minnesota-way). By default, FALSE.
verbose: Print the progress bar in the console. By default, FALSE.
num_thread: Number of threads
x: bvarssvs object
digits: digit option to print
...: not used

Details

SSVS prior gives prior to parameters $\alpha = vec(A)$ (VAR coefficient) and $\Sigma_e^{-1} = \Psi \Psi^T$ (residual covariance).

$$\alpha_j \mid \gamma_j \sim (1 - \gamma_j) N(0, \kappa_{0j}^2) + \gamma_j N(0, \kappa_{1j}^2)$$ $$\gamma_j \sim Bernoulli(q_j)$$

and for upper triangular matrix $\Psi$,

$$\psi_{jj}^2 \sim Gamma(shape = a_j, rate = b_j)$$ $$\psi_{ij} \mid w_{ij} \sim (1 - w_{ij}) N(0, \kappa_{0,ij}^2) + w_{ij} N(0, \kappa_{1,ij}^2)$$ $$w_{ij} \sim Bernoulli(q_{ij})$$

References

George, E. I., & McCulloch, R. E. (1993). Variable Selection via Gibbs Sampling. Journal of the American Statistical Association, 88(423), 881-889.

George, E. I., Sun, D., & Ni, S. (2008). Bayesian stochastic search for VAR model restrictions. Journal of Econometrics, 142(1), 553-580.

Koop, G., & Korobilis, D. (2009). Bayesian Multivariate Time Series Methods for Empirical Macroeconomics. Foundations and Trends® in Econometrics, 3(4), 267-358.