bvartools (version 0.1.0)

bvar: Bayesian Vector Autoregression Objects

Description

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

Forecasting a Bayesian VAR object of class "bvar" with credible bands.

Usage

bvar(
  data = NULL,
  exogen = NULL,
  y = NULL,
  x = NULL,
  A0 = NULL,
  A = NULL,
  B = NULL,
  C = NULL,
  Sigma = NULL
)
# S3 method for bvar
predict(object, ..., n.ahead = 10, new_x = NULL, new_d = NULL, ci = 0.95)

Arguments

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 gen_var.

x

a time-series object of \((pK + (1+s)M + N)\) regressor variables, usually, a result of a call to gen_var.

A0

either a \(K^2 \times S\) matrix of MCMC coefficient draws of structural parameters or a named list, where element coeffs contains a \(K^2 \times S\) matrix of MCMC coefficient draws of structural parameters and element lambda contains the corresponding draws of inclusion parameters in case variable selection algorithms were employed.

A

either a \(pK^2 \times S\) matrix of MCMC coefficient draws of lagged endogenous variables or a named list, where element coeffs contains a \(pK^2 \times S\) matrix of MCMC coefficient draws of lagged endogenous variables and element lambda contains the corresponding draws of inclusion parameters in case variable selection algorithms were employed.

B

either a \(((1 + s)MK) \times S\) matrix of MCMC coefficient draws of unmodelled, non-deterministic variables or a named list, where element coeffs contains a \(((1 + s)MK) \times S\) matrix of MCMC coefficient draws of unmodelled, non-deterministic variables and element lambda contains the corresponding draws of inclusion parameters in case variable selection algorithms were employed.

C

either a \(KN \times S\) matrix of MCMC coefficient draws of deterministic terms or a named list, where element coeffs contains a \(KN \times S\) matrix of MCMC coefficient draws of deterministic terms and element lambda contains the corresponding draws of inclusion parameters in case variable selection algorithms were employed.

Sigma

a \(K^2 \times S\) matrix of MCMC draws for the error variance-covariance matrix or a named list, where element coeffs contains a \(K^2 \times S\) matrix of MCMC draws for the error variance-covariance matrix and element lambda contains the corresponding draws of inclusion parameters in case variable selection algorithms were employed to the covariances.

object

an object of class "bvar", usually, a result of a call to bvar or bvec_to_bvar.

...

additional arguments.

n.ahead

number of steps ahead at which to predict.

new_x

a matrix of new non-deterministic, exogenous variables. Must have n.ahead rows.

new_d

a matrix of new deterministic variables. Must have n.ahead rows.

ci

a numeric between 0 and 1 specifying the probability mass covered by the credible intervals. Defaults to 0.95.

Value

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".

Details

For the VARX model $$A_0 y_t = \sum_{i = 1}^{p} A_i y_{t-i} + \sum_{i = 0}^{s} B_i x_{t - i} + C d_t + u_t$$ 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 \(u_t \sim N(0, \Sigma_u)\).

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 $$A_0 y_t = \sum_{i = 1}^{p} A_{i} y_{t-i} + \sum_{i = 0}^{s} B_{i} x_{t-i} + C D_t + u_t,$$ with \(u_t \sim N(0, \Sigma)\) the function produces n.ahead forecasts.

References

L<U+00FC>tkepohl, H. (2006). New introduction to multiple time series analysis (2nd ed.). Berlin: Springer.

Examples

# NOT RUN {
# 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)

# }