Bayesian Vector Autoregression Objects
bvar is used to create objects of class "bvar".
Forecasting a Bayesian VAR object of class "bvar" with credible bands.
bvar( data = NULL, exogen = NULL, y = NULL, x = NULL, A0 = NULL, A = NULL, B = NULL, C = NULL, Sigma = NULL ) ## S3 method for class 'bvar' predict(object, ..., n.ahead = 10, new_x = NULL, new_d = NULL, ci = 0.95)
data |
the original time-series object of endogenous variables. |
exogen |
the original time-series object of unmodelled variables. |
y |
a time-series object of endogenous variables,
usually, a result of a call to |
x |
a time-series object of (pK + (1+s)M + N) regressor variables, usually, a result of a
call to |
A0 |
either a K^2 \times S matrix of MCMC coefficient draws of structural parameters or
a named list, where element |
A |
either a pK^2 \times S matrix of MCMC coefficient draws of lagged endogenous variables or
a named list, where element |
B |
either a ((1 + s)MK) \times S matrix of MCMC coefficient draws of unmodelled, non-deterministic variables
or a named list, where element |
C |
either a KN \times S matrix of MCMC coefficient draws of deterministic terms 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 |
object |
an object of class |
... |
additional arguments. |
n.ahead |
number of steps ahead at which to predict. |
new_x |
an object of class |
new_d |
a matrix of new deterministic variables. Must have |
ci |
a numeric between 0 and 1 specifying the probability mass covered by the credible intervals. Defaults to 0.95. |
For the VARX model
A_0 y_t = ∑_{i = 1}^{p} A_i y_{t-i} + ∑_{i = 0}^{s} B_i x_{t - i} + C d_t + u_t
the function collects the S draws of a Gibbs sampler (after the burn-in phase) in a standardised object, where y_t is a K-dimensional vector of endogenous variables, A_0 is a K \times K matrix of structural coefficients. A_i is a K \times K coefficient matrix of lagged endogenous variabels. x_t is an M-dimensional vector of unmodelled, non-deterministic variables and B_i its corresponding coefficient matrix. d_t is an N-dimensional vector of deterministic terms and C its 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 A0, A,
B, C and Sigma have to correspond to the same MCMC iterations.
For the VAR model
A_0 y_t = ∑_{i = 1}^{p} A_{i} y_{t-i} + ∑_{i = 0}^{s} B_{i} x_{t-i} + C D_t + u_t,
with u_t \sim N(0, Σ) the function produces n.ahead forecasts.
An object of class "bvar" 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 endogenous variables. |
x |
a (pK + (1+s)M + N) \times T matrix of regressor variables. |
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 structural parameters. |
A |
an S \times pK^2 "mcmc" object of coefficient draws of lagged endogenous variables. |
A_lambda |
an S \times pK^2 "mcmc" object of inclusion parameters for lagged endogenous variables. |
B |
an S \times ((1 + s)MK) "mcmc" object of coefficient draws of unmodelled, non-deterministic variables. |
B_lambda |
an S \times ((1 + s)MK) "mcmc" object of inclusion parameters for unmodelled, non-deterministic variables. |
C |
an S \times NK "mcmc" object of coefficient draws of deterministic terms. |
C_lambda |
an S \times NK "mcmc" object of inclusion parameters for deterministic terms. |
Sigma |
an S \times K^2 "mcmc" object of variance-covariance draws. |
Sigma_lambda |
an S \times K^2 "mcmc" object of inclusion parameters for error covariances. |
specifications |
a list containing information on the model specification. |
A time-series object of class "bvarprd".
Lütkepohl, H. (2006). New introduction to multiple time series analysis (2nd ed.). Berlin: Springer.
# Get data
data("e1")
e1 <- diff(log(e1))
e1 <- window(e1, end = c(1978, 4))
# Generate model data
data <- gen_var(e1, p = 2, deterministic = "const")
# Add priors
model <- add_priors(data,
coef = list(v_i = 0, v_i_det = 0),
sigma = list(df = 0, scale = .00001))
# Set RNG seed for reproducibility
set.seed(1234567)
iterations <- 400 # Number of iterations of the Gibbs sampler
# Chosen number of iterations and burnin should be much higher.
burnin <- 100 # Number of burn-in draws
draws <- iterations + burnin # Total number of MCMC draws
y <- t(model$data$Y)
x <- t(model$data$Z)
tt <- ncol(y) # Number of observations
k <- nrow(y) # Number of endogenous variables
m <- k * nrow(x) # Number of estimated coefficients
# Priors
a_mu_prior <- model$priors$coefficients$mu # Vector of prior parameter means
a_v_i_prior <- model$priors$coefficients$v_i # Inverse of the prior covariance matrix
u_sigma_df_prior <- model$priors$sigma$df # Prior degrees of freedom
u_sigma_scale_prior <- model$priors$sigma$scale # Prior covariance matrix
u_sigma_df_post <- tt + u_sigma_df_prior # Posterior degrees of freedom
# Initial values
u_sigma_i <- diag(1 / .00001, k)
# Data containers for posterior draws
draws_a <- matrix(NA, m, iterations)
draws_sigma <- matrix(NA, k^2, iterations)
# Start Gibbs sampler
for (draw in 1:draws) {
# Draw conditional mean parameters
a <- post_normal(y, x, u_sigma_i, a_mu_prior, a_v_i_prior)
# Draw variance-covariance matrix
u <- y - matrix(a, k) %*% x # Obtain residuals
u_sigma_scale_post <- solve(u_sigma_scale_prior + tcrossprod(u))
u_sigma_i <- matrix(rWishart(1, u_sigma_df_post, u_sigma_scale_post)[,, 1], k)
# Store draws
if (draw > burnin) {
draws_a[, draw - burnin] <- a
draws_sigma[, draw - burnin] <- solve(u_sigma_i)
}
}
# Generate bvar object
bvar_est <- bvar(y = model$data$Y, x = model$data$Z,
A = draws_a[1:18,], C = draws_a[19:21, ],
Sigma = draws_sigma)
# Load data
data("e1")
e1 <- diff(log(e1)) * 100
e1 <- window(e1, end = c(1978, 4))
# Generate model data
model <- gen_var(e1, p = 2, deterministic = 2,
iterations = 100, burnin = 10)
# Chosen number of iterations and burnin should be much higher.
# Add prior specifications
model <- add_priors(model)
# Obtain posterior draws
object <- draw_posterior(model)
# Generate forecasts
bvar_pred <- predict(object, n.ahead = 10, new_d = rep(1, 10))
# Plot forecasts
plot(bvar_pred)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.