# bvec

0th

Percentile

##### Bayesian Vector Error Correction Objects

bvec is used to create objects of class "bvec".

##### Usage
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)
##### Arguments
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 gen_vec.

w

a $(K + M + N^{R}) \times T$ matrix of variables in the cointegration term, usually, a result of a call to gen_vec.

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 gen_vec.

alpha

a $Kr \times S$ matrix of MCMC coefficient draws of the loading matrix $\alpha$.

beta

a $((K + M + N^{R})r) \times S$ matrix of MCMC coefficient draws of cointegration matrix $\beta$.

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.

##### Details

For the VECX model $$\Delta y_t = \Pi^{+} \begin{pmatrix} y_{t-1} \\ x_{t-1} \\ d^{R}_{t-1} \end{pmatrix} + \sum_{i = 1}^{p-1} \Gamma_i \Delta y_{t-i} + \sum_{i = 0}^{s-1} \Upsilon_i \Delta x_{t-i} + C^{UR} d^{UR}_t + A_0^{-1} u_t$$ the function collects the S draws of a Gibbs sampler (after the burn-in phase) in a standardised object, where $\Delta y_t$ is a K-dimensional vector of differenced endogenous variables and $A_0$ is a $K \times K$ matrix of structural coefficients. $\Pi^{+} = \left[ \Pi, \Pi^{x}, \Pi^{d} \right]$ 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. $\Pi$, $\Pi^{x}$, and $\Pi^{d}$ are the corresponding coefficient matrices, respectively. $\Gamma_i$ is a coefficient matrix of lagged differenced endogenous variabels. $\Delta x_t$ is an M-dimensional vector of unmodelled, non-deterministic variables and $\Upsilon_i$ 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 $u_t \sim N(0, \Sigma_u)$.

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.

##### Value

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.

• bvec
##### Examples
# NOT RUN {
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)

# }

Documentation reproduced from package bvartools, version 0.0.1, License: GPL (>= 2)

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