R: Fitting Bayesian VAR(p) of SSVS Prior

bvar_ssvs {bvhar}

R Documentation

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

## S3 method for class 'bvarssvs'
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 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})

Gibbs sampler is used for the estimation. See ssvs_bvar_algo how it works.

Value

bvar_ssvs returns an object named bvarssvs class. It is a list with the following components:

alpha_record: MCMC trace for vectorized coefficients (alpha \alpha) with posterior::draws_df format.
eta_record: MCMC trace for upper triangular element of cholesky factor (eta \eta) with posterior::draws_df format.
psi_record: MCMC trace for diagonal element of cholesky factor (psi \psi) with posterior::draws_df format.
omega_record: MCMC trace for indicator variable for eta (omega \omega) with posterior::draws_df format.
gamma_record: MCMC trace for indicator variable for alpha (gamma \gamma) with posterior::draws_df format.
chol_record: MCMC trace for cholesky factor matrix \Psi with list format.
ols_coef: OLS estimates for VAR coefficients.
ols_cholesky: OLS estimates for cholesky factor
coefficients: Posterior mean of VAR coefficients.
omega_posterior: Posterior mean of omega
pip: Posterior inclusion probability
param: posterior::draws_df with every variable: alpha, eta, psi, omega, and gamma
chol_posterior: Posterior mean of cholesky factor matrix
covmat: Posterior mean of covariance matrix
df: Numer of Coefficients: mp + 1 or mp
p: Lag of VAR
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. "VAR_SSVS"
type: include constant term ("const") or not ("none")
spec: SSVS specification defined by set_ssvs()
init: Initial specification defined by init_ssvs()
iter: Total iterations
burn: Burn-in
thin: Thinning
chain: The numer of chains
y0: Y_0
design: X_0
y: Raw input

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.