Conditional forecasts from a fitted steady-state BVAR model

Computes and plots conditional forecasts from a fitted steady-state bvar object. Conditions are imposed on specific variables at specific horizons using Algorithm 3.3.1 from Dieppe, Legrand, and van Roye (2016). Both conditional and unconditional forecasts are plotted for comparison. Please note that for the moment, conditional forecasting is only enabled for the homoscedastic steady-state BVAR, i.e. when SV=FALSE in priors().

Usage

conditional_forecast(
  bvar_obj,
  conditions,
  pi = 0.95,
  fcst_type = c("mean", "median"),
  growth_rate_idx = NULL,
  plot_idx = NULL
)

Arguments

bvar_obj

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

conditions

A data frame with three columns: var (integer index of the conditioned variable), horizon (integer forecast horizon at which the condition is imposed), and value (numeric, the imposed condition). Note that var and horizon must be integers, as they are used for indexing.

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 \(\ln x_{t} - \ln x_{t-f}\), where \(f\) is the frequency of the data (4 for quarterly, 12 for monthly). Only suitable for variables specified as \(\ln x_{t} - \ln x_{t-1}\), i.e. diff(log(x)) or 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.

Value

Invisibly returns a list with three matrices: forecast, lower, and upper, each of dimension H x k.

Details

See Section 5.3 of Dieppe, Legrand, and van Roye (2016) for more details. Please note the limitations of this method, see the detailed discussion in Section 5.4 of Dieppe, Legrand, and van Roye (2016).

References

Dieppe, A., Legrand, R., and van Roye, B. (2016). The BEAR toolbox. Working Paper Series, No. 1934. European Central Bank.

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,
                   SV = FALSE,
                   SV_type = NULL,
                   SV_priors = NULL)
                   
bvar_obj <- fit(bvar_obj,
                H = 8,
                d_pred = matrix(rep(1,8)),
                iter = 200,
                warmup = 50,
                chains = 1,
                cores = 1)
#> 
#> SAMPLING FOR MODEL 'steady_state_bvar_homoscedastic_jeffreys_prior' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 7.8e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.78 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: 0.033 seconds (Warm-up)
#> Chain 1:                0.098 seconds (Sampling)
#> Chain 1:                0.131 seconds (Total)
#> Chain 1: 
#> 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
                
conditions <- data.frame(var = rep(2,8),
                         horizon = rep(1:8),
                         value   = rep(1,8))
                         
(cond_fcst <- conditional_forecast(bvar_obj,
                                  conditions,
                                  pi=0.68,
                                  fcst_type = "mean"))


#> $forecast
#>             [,1] [,2]
#> [1,]  0.14441447    1
#> [2,] -0.12757620    1
#> [3,]  0.10365391    1
#> [4,]  0.04508464    1
#> [5,] -0.12616706    1
#> [6,] -0.01333035    1
#> [7,] -0.06550231    1
#> [8,] -0.26327988    1
#> 
#> $lower
#>           [,1] [,2]
#> [1,] -1.283297    1
#> [2,] -1.594437    1
#> [3,] -1.220475    1
#> [4,] -1.333708    1
#> [5,] -1.497314    1
#> [6,] -1.494692    1
#> [7,] -1.538898    1
#> [8,] -1.795598    1
#> 
#> $upper
#>          [,1] [,2]
#> [1,] 1.553397    1
#> [2,] 1.202902    1
#> [3,] 1.624368    1
#> [4,] 1.453796    1
#> [5,] 1.414222    1
#> [6,] 1.431886    1
#> [7,] 1.554301    1
#> [8,] 1.269970    1
#> 
# }