bvec {bvartools} | R Documentation |
'bvec' is used to create objects of class "bvec".
bvec(data = NULL, exogen = NULL, y = NULL, w = NULL, x = NULL, alpha = NULL, beta = NULL, Pi = NULL, Pi_x = NULL, Pi_d = NULL, A0 = NULL, Gamma = NULL, Upsilon = NULL, C = NULL, Sigma = NULL)
data |
the original time-series object of endogenous variables. |
exogen |
the original time-series object of unmodelled variables. |
y |
a K \times T matrix of differenced endogenous variables,
usually, a result of a call to |
w |
a (K + M + N^{R}) \times T matrix of variables in the
cointegration term, usually, a result of a call to |
x |
a (K(p - 1) + Ms + N^{UR}) \times T matrix of differenced regressors
of y and x, and unrestricted deterministic terms, 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. |
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. |
A0 |
a K^2 \times S matrix of MCMC coefficient draws of structural parameters. |
Gamma |
a (p-1)K^2 \times S matrix of MCMC coefficient draws of differenced lagged endogenous variables. |
Upsilon |
an sMK \times S matrix of MCMC coefficient draws of differenced unmodelled variables. |
C |
an KN^{UR} \times S matrix of MCMC coefficient draws of unrestricted deterministic terms. |
Sigma |
a K^2 \times S matrix of variance-covariance MCMC draws. |
For the VECX model
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 + A_0^{-1} u_t
the function collects the S draws of a Gibbs sampler (after the burn-in phase) 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 K \times T matrix of differenced endogenous variables. |
w |
a (K + M + N^{R}) \times T matrix of variables in the cointegration term. |
x |
a ((p - 1)K + sM + N^{UR}) \times T matrix of differenced regressor variables and unrestricted deterministic terms. |
A0 |
an S \times K^2 "mcmc" object of coefficient draws of 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. |
Upsilon |
an S \times sMK "mcmc" object of coefficient draws of differenced unmodelled variables. |
C |
an S \times KN^{UR} "mcmc" object of coefficient draws of deterministic terms. |
Sigma |
an S \times K^2 "mcmc" object of variance-covariance draws. |
specifications |
a list containing information on the model specification. |
data("e6") data <- gen_vec(e6, p = 4, const = "unrestricted", season = "unrestricted") y <- data$Y w <- data$W x <- data$X # Reset random number generator for reproducibility set.seed(1234567) iter <- 500 # Number of iterations of the Gibbs sampler # Chosen number of iterations should be much higher, e.g. 30000. burnin <- 100 # Number of burn-in draws store <- iter - burnin r <- 1 # Set rank t <- ncol(y) # Number of observations k <- nrow(y) # Number of endogenous variables k_w <- nrow(w) # Number of regressors in error correction term k_x <- nrow(x) # Number of differenced regressors and unrestrictec deterministic terms k_alpha <- k * r # Number of elements in alpha k_beta <- k_w * r # Number of elements in beta k_gamma <- k * k_x # Set uninformative priors a_mu_prior <- matrix(0, k_x * k) # Vector of prior parameter means a_v_i_prior <- diag(0, k_x * k) # Inverse of the prior covariance matrix v_i <- 0 p_tau_i <- diag(1, k_w) u_sigma_df_prior <- r # Prior degrees of freedom u_sigma_scale_prior <- diag(0, k) # Prior covariance matrix u_sigma_df_post <- t + u_sigma_df_prior # Posterior degrees of freedom # Initial values beta <- matrix(c(1, -4), k_w, r) u_sigma_i <- diag(.0001, k) u_sigma <- solve(u_sigma_i) g_i <- u_sigma_i # Data containers draws_alpha <- matrix(NA, k_alpha, store) draws_beta <- matrix(NA, k_beta, store) draws_pi <- matrix(NA, k * k_w, store) draws_gamma <- matrix(NA, k_gamma, store) draws_sigma <- matrix(NA, k^2, store) # Start Gibbs sampler for (draw in 1:iter) { # Draw conditional mean parameters temp <- post_coint_kls(y = y, beta = beta, w = w, x = x, sigma_i = u_sigma_i, v_i = v_i, p_tau_i = p_tau_i, g_i = g_i, gamma_mu_prior = a_mu_prior, gamma_V_i_prior = a_v_i_prior) alpha <- temp$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 = y, w = w, x = x, Pi = draws_pi, Gamma = draws_gamma[1:k_nondet,], C = draws_gamma[(k_nondet + 1):nrow(draws_gamma),], Sigma = draws_sigma)