Bayesian Vector Error Correction Objects
'bvec' is used to create objects of class "bvec".
bvec( y, alpha = NULL, beta = NULL, r = NULL, Pi = NULL, Pi_x = NULL, Pi_d = NULL, w = NULL, w_x = NULL, w_d = NULL, Gamma = NULL, Upsilon = NULL, C = NULL, x = NULL, x_x = NULL, x_d = NULL, A0 = NULL, Sigma = NULL, data = NULL, exogen = NULL )
y |
a time-series object of differenced endogenous variables,
usually, a result of a call to |
alpha |
a Kr \times S matrix of MCMC coefficient draws of the loading matrix α. |
beta |
a ((K + M + N^{R})r) \times S matrix of MCMC coefficient draws of cointegration matrix β. |
r |
an integer of the rank of the cointegration matrix. |
Pi |
a K^2 \times S matrix of MCMC coefficient draws of endogenous varaibles in the cointegration matrix. |
Pi_x |
a KM \times S matrix of MCMC coefficient draws of unmodelled, non-deterministic variables in the cointegration matrix. |
Pi_d |
a KN^{R} \times S matrix of MCMC coefficient draws of restricted deterministic terms. |
w |
a time-series object of lagged endogenous variables in levels, which enter the
cointegration term, usually, a result of a call to |
w_x |
a time-series object of lagged unmodelled, non-deterministic variables in levels, which enter the
cointegration term, usually, a result of a call to |
w_d |
a time-series object of deterministic terms, which enter the
cointegration term, usually, a result of a call to |
Gamma |
a (p-1)K^2 \times S matrix of MCMC coefficient draws of differenced lagged endogenous variables or
a named list, where element |
Upsilon |
an sMK \times S matrix of MCMC coefficient draws of differenced unmodelled, non-deterministic variables or
a named list, where element |
C |
an KN^{UR} \times S matrix of MCMC coefficient draws of unrestricted deterministic terms or
a named list, where element |
x |
a time-series object of K(p - 1) differenced endogenous variables. |
x_x |
a time-series object of Ms differenced unmodelled regressors. |
x_d |
a time-series object of N^{UR} deterministic terms that do not enter the cointegration term. |
A0 |
either a K^2 \times S matrix of MCMC coefficient draws of structural parameters or
a named list, where element |
Sigma |
a K^2 \times S matrix of MCMC draws for the error variance-covariance matrix or
a named list, where element |
data |
the original time-series object of endogenous variables. |
exogen |
the original time-series object of unmodelled variables. |
For the vector error correction model with unmodelled exogenous variables (VECX)
A_0 Δ y_t = Π^{+} \begin{pmatrix} y_{t-1} \\ x_{t-1} \\ d^{R}_{t-1} \end{pmatrix} + ∑_{i = 1}^{p-1} Γ_i Δ y_{t-i} + ∑_{i = 0}^{s-1} Υ_i Δ x_{t-i} + C^{UR} d^{UR}_t + u_t
the function collects the S draws of a Gibbs sampler in a standardised object, where Δ y_t is a K-dimensional vector of differenced endogenous variables and A_0 is a K \times K matrix of structural coefficients. Π^{+} = ≤ft[ Π, Π^{x}, Π^{d} \right] is the coefficient matrix of the error correction term, where y_{t-1}, x_{t-1} and d^{R}_{t-1} are the first lags of endogenous, exogenous variables in levels and restricted deterministic terms, respectively. Π, Π^{x}, and Π^{d} are the corresponding coefficient matrices, respectively. Γ_i is a coefficient matrix of lagged differenced endogenous variabels. Δ x_t is an M-dimensional vector of unmodelled, non-deterministic variables and Υ_i its corresponding coefficient matrix. d_t is an N^{UR}-dimensional vector of unrestricted deterministics and C^{UR} the corresponding coefficient matrix. u_t is an error term with u_t \sim N(0, Σ_u).
The draws of the different coefficient matrices provided in alpha, beta,
Pi, Pi_x, Pi_d, A0, Gamma, Ypsilon,
C and Sigma have to correspond to the same MCMC iteration.
An object of class "gvec" containing the following components, if specified:
data |
the original time-series object of endogenous variables. |
exogen |
the original time-series object of unmodelled variables. |
y |
a time-series object of differenced endogenous variables. |
w |
a time-series object of lagged endogenous variables in levels, which enter the cointegration term. |
w_x |
a time-series object of lagged unmodelled, non-deterministic variables in levels, which enter the cointegration term. |
w_d |
a time-series object of deterministic terms, which enter the cointegration term. |
x |
a time-series object of K(p - 1) differenced endogenous variables |
x_x |
a time-series object of Ms differenced unmodelled regressors. |
x_d |
a time-series object of N^{UR} deterministic terms that do not enter the cointegration term. |
A0 |
an S \times K^2 "mcmc" object of coefficient draws of structural parameters. |
A0_lambda |
an S \times K^2 "mcmc" object of inclusion parameters for coefficients corresponding to structural parameters. |
alpha |
an S \times Kr "mcmc" object of coefficient draws of loading parameters. |
beta |
an S \times ((K + M + N^{R})r) "mcmc" object of coefficient draws of cointegration parameters. |
Pi |
an S \times K^2 "mcmc" object of coefficient draws of endogenous variables in the cointegration matrix. |
Pi_x |
an S \times KM "mcmc" object of coefficient draws of unmodelled, non-deterministic variables in the cointegration matrix. |
Pi_d |
an S \times KN^{R} "mcmc" object of coefficient draws of unrestricted deterministic variables in the cointegration matrix. |
Gamma |
an S \times (p-1)K^2 "mcmc" object of coefficient draws of differenced lagged endogenous variables. |
Gamma_lamba |
an S \times (p-1)K^2 "mcmc" object of inclusion parameters for coefficients corresponding to differenced lagged endogenous variables. |
Upsilon |
an S \times sMK "mcmc" object of coefficient draws of differenced unmodelled variables. |
Upsilon_lambda |
an S \times sMK "mcmc" object of inclusion parameters for coefficients corresponding to differenced unmodelled, non-deterministic variables. |
C |
an S \times KN^{UR} "mcmc" object of coefficient draws of deterministic terms that do not enter the cointegration term. |
C_lambda |
an S \times KN^{UR} "mcmc" object of inclusion parameters for coefficients corresponding to deterministic terms, that do not enter the conitegration term. |
Sigma |
an S \times K^2 "mcmc" object of variance-covariance draws. |
Sigma_lambda |
an S \times K^2 "mcmc" object inclusion parameters for the variance-covariance matrix. |
specifications |
a list containing information on the model specification. |
# Load data
data("e6")
# Generate model
data <- gen_vec(e6, p = 4, r = 1, const = "unrestricted", season = "unrestricted")
# Obtain data matrices
y <- t(data$data$Y)
w <- t(data$data$W)
x <- t(data$data$X)
# Reset random number generator for reproducibility
set.seed(1234567)
iterations <- 400 # Number of iterations of the Gibbs sampler
# Chosen number of iterations should be much higher, e.g. 30000.
burnin <- 100 # Number of burn-in draws
draws <- iterations + burnin
r <- 1 # Set rank
tt <- ncol(y) # Number of observations
k <- nrow(y) # Number of endogenous variables
k_w <- nrow(w) # Number of regressors in error correction term
k_x <- nrow(x) # Number of differenced regressors and unrestrictec deterministic terms
k_alpha <- k * r # Number of elements in alpha
k_beta <- k_w * r # Number of elements in beta
k_gamma <- k * k_x
# Set uninformative priors
a_mu_prior <- matrix(0, k_x * k) # Vector of prior parameter means
a_v_i_prior <- diag(0, k_x * k) # Inverse of the prior covariance matrix
v_i <- 0
p_tau_i <- diag(1, k_w)
u_sigma_df_prior <- r # Prior degrees of freedom
u_sigma_scale_prior <- diag(0, k) # Prior covariance matrix
u_sigma_df_post <- tt + u_sigma_df_prior # Posterior degrees of freedom
# Initial values
beta <- matrix(c(1, -4), k_w, r)
u_sigma_i <- diag(1 / .0001, k)
g_i <- u_sigma_i
# Data containers
draws_alpha <- matrix(NA, k_alpha, iterations)
draws_beta <- matrix(NA, k_beta, iterations)
draws_pi <- matrix(NA, k * k_w, iterations)
draws_gamma <- matrix(NA, k_gamma, iterations)
draws_sigma <- matrix(NA, k^2, iterations)
# Start Gibbs sampler
for (draw in 1:draws) {
# Draw conditional mean parameters
temp <- post_coint_kls(y = y, beta = beta, w = w, x = x, sigma_i = u_sigma_i,
v_i = v_i, p_tau_i = p_tau_i, g_i = g_i,
gamma_mu_prior = a_mu_prior,
gamma_v_i_prior = a_v_i_prior)
alpha <- temp$alpha
beta <- temp$beta
Pi <- temp$Pi
gamma <- temp$Gamma
# Draw variance-covariance matrix
u <- y - Pi %*% w - matrix(gamma, k) %*% x
u_sigma_scale_post <- solve(tcrossprod(u) +
v_i * alpha %*% tcrossprod(crossprod(beta, p_tau_i) %*% beta, alpha))
u_sigma_i <- matrix(rWishart(1, u_sigma_df_post, u_sigma_scale_post)[,, 1], k)
u_sigma <- solve(u_sigma_i)
# Update g_i
g_i <- u_sigma_i
# Store draws
if (draw > burnin) {
draws_alpha[, draw - burnin] <- alpha
draws_beta[, draw - burnin] <- beta
draws_pi[, draw - burnin] <- Pi
draws_gamma[, draw - burnin] <- gamma
draws_sigma[, draw - burnin] <- u_sigma
}
}
# Number of non-deterministic coefficients
k_nondet <- (k_x - 4) * k
# Generate bvec object
bvec_est <- bvec(y = data$data$Y, w = data$data$W,
x = data$data$X[, 1:6],
x_d = data$data$X[, 7:10],
Pi = draws_pi,
Gamma = draws_gamma[1:k_nondet,],
C = draws_gamma[(k_nondet + 1):nrow(draws_gamma),],
Sigma = draws_sigma)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.