ssvs function

Stochastic Search Variable Selection

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.

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.

Returns

A named list containing two components: - v_i: an $M \times M$ inverse prior covariance matrix.

• lambda: an M-dimensional vector of inclusion parameters.

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

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

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)

References

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