Forecast from a fitted steady-state BVAR model

Computes and plots forecasts from a fitted steady-state bvar object. Draws from the joint predictive distribution are used to construct point forecasts and prediction intervals. Optionally converts monthly or quarterly growth rate forecasts to annual growth rates for variables specified as 100*diff(log(x)). Optionally overlays the posterior steady states.

Usage

forecast(
  x,
  pi = 0.95,
  fcst_type = c("mean", "median"),
  growth_rate_idx = NULL,
  plot_idx = NULL,
  show_all = TRUE,
  ss = TRUE,
  ss_type = c("mean", "median"),
  ss_ci = 0.95
)

Arguments

x

A steady-state bvar object that has been passed through fit.

pi

Numeric. The prediction interval width. Default 0.95, i.e. 95% prediction interval.

fcst_type

Character. Whether to use "mean" or "median" as the point forecast. Default "mean".

growth_rate_idx

Integer vector. Indices of variables of which to convert forecasts to annual growth rates \(100 (\ln x_{t} - \ln x_{t-f})\), where \(f\) is the frequency of the data (4 for quarterly, 12 for monthly). Only suitable for variables specified as \(100 (\ln x_{t} - \ln x_{t-1})\), i.e. 100*diff(log(x)). Computed by summing up to \(f\) log first differences. Default is NULL.

plot_idx

Integer vector. Indices of variables to plot. If NULL (default), all variables are plotted. Forecasts are always computed and returned for all variables, regardless of plot_idx.

show_all

Logical. If TRUE (default), the full history is shown. If FALSE, the last eight years of history are shown.

ss

Logical. If TRUE, overlays the posterior steady state \(\mu_t = \Psi d_t\). Default TRUE. For variables in growth_rate_idx, the posterior steady-state is annualized.

ss_type

Character. Whether to use "mean" or "median" of the posterior as the steady-state point estimate. Default "mean".

ss_ci

Numeric. The posterior credible interval width for the steady state. Default 0.95, i.e. 95% credible interval.

Value

Invisibly returns a list with three matrices: forecast, lower, and upper, each of dimension H x k where H is the forecast horizon and k is the number of variables.

Examples

# \donttest{
#homoscedastic with Jeffreys prior
yt <- matrix(rnorm(50), 25, 2)

bvar_obj <- bvar(data = yt)

bvar_obj <- setup(bvar_obj, p=1, deterministic = "constant")

bvar_obj <- priors(bvar_obj,
                   lambda_1 = 0.2,
                   lambda_2 = 0.5,
                   lambda_3 = 1,
                   first_own_lag_prior_mean = rep(1,2),
                   theta_Psi = rep(0, 2),
                   Omega_Psi = diag(0.1, 2, 2),
                   Jeffreys = TRUE)
                   
bvar_obj <- fit(bvar_obj,
                H = 8,
                iter = 200,
                warmup = 50,
                chains = 1,
                cores = 1)
#> ------------------------------------------------------------
#> Forecast horizon:
#> 8
#> 
#> Future deterministic variables (d_pred):
#>     constant
#> h=1        1
#> h=2        1
#> h=3        1
#> h=4        1
#> h=5        1
#> h=6        1
#> h=7        1
#> h=8        1
#> ------------------------------------------------------------
#> Estimating Stan model:
#> steady_state_bvar_homoscedastic_jeffreys_prior
#> 
#> Also generating draws from the joint predictive distribution
#> 
#> ...
#> 
#> SAMPLING FOR MODEL 'steady_state_bvar_homoscedastic_jeffreys_prior' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 5.8e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.58 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: WARNING: There aren't enough warmup iterations to fit the
#> Chain 1:          three stages of adaptation as currently configured.
#> Chain 1:          Reducing each adaptation stage to 15%/75%/10% of
#> Chain 1:          the given number of warmup iterations:
#> Chain 1:            init_buffer = 7
#> Chain 1:            adapt_window = 38
#> Chain 1:            term_buffer = 5
#> Chain 1: 
#> Chain 1: Iteration:   1 / 200 [  0%]  (Warmup)
#> Chain 1: Iteration:  20 / 200 [ 10%]  (Warmup)
#> Chain 1: Iteration:  40 / 200 [ 20%]  (Warmup)
#> Chain 1: Iteration:  51 / 200 [ 25%]  (Sampling)
#> Chain 1: Iteration:  70 / 200 [ 35%]  (Sampling)
#> Chain 1: Iteration:  90 / 200 [ 45%]  (Sampling)
#> Chain 1: Iteration: 110 / 200 [ 55%]  (Sampling)
#> Chain 1: Iteration: 130 / 200 [ 65%]  (Sampling)
#> Chain 1: Iteration: 150 / 200 [ 75%]  (Sampling)
#> Chain 1: Iteration: 170 / 200 [ 85%]  (Sampling)
#> Chain 1: Iteration: 190 / 200 [ 95%]  (Sampling)
#> Chain 1: Iteration: 200 / 200 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 0.015 seconds (Warm-up)
#> Chain 1:                0.044 seconds (Sampling)
#> Chain 1:                0.059 seconds (Total)
#> Chain 1: 
#> Warning: The largest R-hat is NA, indicating chains have not mixed.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#r-hat
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
#> SAMPLING FINISHED
                
forecast(bvar_obj,
         fcst_type = "mean",
         pi = 0.90,
         show_all = TRUE,
         ss = TRUE,
         ss_type = "mean",
         ss_ci = 0.95)


# }