ssvs {bvartools}

Stochastic Search Variable Selection

Description

ssvs employs stochastic search variable selection as proposed by George et al. (2008) to produce a draw of the precision matrix of the coefficients in a VAR model.

Usage

ssvs(a, tau0, tau1, prob_prior, include = NULL)

Arguments

a

an M-dimensional vector of coefficient draws.

tau0

an M-dimensional vector of prior standard deviations for restricted coefficients in vector a.

tau1

an M-dimensional vector of prior standard deviations for unrestricted coefficients in vector a.

prob_prior

an M-dimensional vector of prior inclusion probabilites for the coefficients in vector a.

include

an integer vector specifying the positions of coefficients in vector a, which should be included in the SSVS algorithm. If NULL (default), SSVS will be applied to all coefficients.

Details

The function employs stochastic search variable selection (SSVS) as proposed by George et al. (2008) to produce a draw of the diagonal inverse prior covariance matrix \underline{V}^{-1} and the corresponding vector of inclusion parameters \lambda of the vectorised coefficient matrix a = vec(A) for the VAR model

y_t = A x_t + u_t,

where y_{t} is a K-dimensional vector of endogenous variables, x_{t} is a vector of explanatory variabes and the error term is u_t \sim \Sigma.

Value

A named list containing two components:

v_i

an M \times M inverse prior covariance matrix.

lambda

an M-dimensional vector of inclusion parameters.

References

George, E. I., Sun, D., & Ni, S. (2008). Bayesian stochastic search for VAR model restrictions. Journal of Econometrics, 142(1), 553–580. doi:10.1016/j.jeconom.2007.08.017

Examples

# Load data
data("e1")
data <- diff(log(e1))

# Generate model data
temp <- gen_var(data, p = 2, deterministic = "const")
y <- t(temp$data$Y)
x <- t(temp$data$Z)
k <- nrow(y)
tt <- ncol(y)
m <- k * nrow(x)

# Obtain SSVS priors using the semiautomatic approach
priors <- ssvs_prior(temp, semiautomatic = c(0.1, 10))
tau0 <- priors$tau0
tau1 <- priors$tau1

# Prior for inclusion parameter
prob_prior <- matrix(0.5, m)

# Priors
a_mu_prior <- matrix(0, m)
a_v_i_prior <- diag(c(tau1^2), m)

# Initial value of Sigma
sigma_i <- solve(tcrossprod(y) / tt)

# Draw parameters
a <- post_normal(y = y, x = x, sigma_i = sigma_i,
                 a_prior = a_mu_prior, v_i_prior = a_v_i_prior)

# Run SSVS
lambda <- ssvs(a = a, tau0 = tau0, tau1 = tau1,
               prob_prior = prob_prior)