Bootstrap Uncertainty and Scenario Forecasting

Overview

bridgr can return point forecasts only, or it can also compute bootstrap uncertainty for the fitted target equation and predictive intervals for forecasts.

The relevant estimation arguments are:

se = FALSE: point forecasts only.
se = TRUE: compute bootstrap coefficient uncertainty and predictive forecast intervals.
bootstrap = list(type = "block", N = 100, block_length = NULL): control the bootstrap.

At the moment, "block" is the only supported bootstrap type.

Fitting a Model with Bootstrap Uncertainty

gdp_growth <- suppressMessages(tsbox::ts_na_omit(tsbox::ts_pc(gdp)))

boot_model <- bridge(
  target = gdp_growth,
  indic = baro,
  indic_predict = "auto.arima",
  indic_aggregators = "mean",
  indic_lags = 1,
  target_lags = 1,
  h = 2,
  se = TRUE,
  bootstrap = list(type = "block", N = 20, block_length = NULL)
)

The current implementation uses a conditional block bootstrap on the final target-frequency estimation sample. It does not re-estimate indicator forecast models or parametric aggregation weights inside each bootstrap draw, but it does add simulated future target shocks to the stored forecast draws.

Forecast Output

Once the model has been estimated with se = TRUE, forecast() returns a standardized forecast object with:

mean
se
lower
upper
forecast_set
bootstrap metadata

fc <- forecast(boot_model)

fc
#> Bridge forecast
#> -----------------------------------
#> Target series: gdp_growth
#> Forecast horizon: 2
#> Uncertainty: predictive intervals from conditional block bootstrap
#> Bootstrap draws: 20 / 20
#> Block length: 5
#> -----------------------------------
#>   time       mean  se    lower_80 upper_80 lower_95 upper_95
#> 1 2023-01-01 0.972 0.947 -0.499   2.440    -0.524   2.775   
#> 2 2023-04-01 0.698 0.571 -0.190   1.378    -0.529   1.578
fc$bootstrap
#> $enabled
#> [1] TRUE
#> 
#> $type
#> [1] "block"
#> 
#> $N
#> [1] 20
#> 
#> $valid_N
#> [1] 20
#> 
#> $block_length
#> [1] 5
#> 
#> $conditional
#> [1] TRUE

The intervals are empirical predictive intervals based on the stored bootstrap forecast draws.

Summary Output

The same bootstrap run also feeds into summary().

summary(boot_model)
#> Bridge model summary
#> -----------------------------------
#> Target series: gdp_growth
#> Target frequency: quarter
#> Forecast horizon: 2
#> Estimation rows: 74
#> Regressors: baro, baro_lag1
#> -----------------------------------
#> Target equation coefficients:
#>           Estimate Bootstrap SE
#> ar1          0.243        0.162
#> intercept   -6.493        1.730
#> baro         0.161        0.045
#> baro_lag1   -0.092        0.038
#> -----------------------------------
#> Indicator summary:
#>      Frequency Predict    Aggregation
#> baro month     auto.arima mean       
#> -----------------------------------
#> Uncertainty:
#> Method: conditional block bootstrap with predictive forecast draws
#> Bootstrap draws: 20 / 20
#> Block length: 5
#> -----------------------------------

The printed summary keeps the same base layout as a point-estimate model and adds the uncertainty section only when bootstrap output is available.

Scenario Forecasting with `xreg`

If you want to forecast the target under a different future regressor path, pass a custom xreg object to forecast(). The custom regressor names must match the ones used in the fitted target equation.

scenario_xreg <- dplyr::tibble(
  id = rep(boot_model$regressor_names, each = nrow(boot_model$forecast_set)),
  time = rep(
    boot_model$forecast_set$time,
    times = length(boot_model$regressor_names)
  ),
  value = c(
    boot_model$forecast_set$baro + 5,
    boot_model$forecast_set$baro_lag1 + 5
  )
)

scenario_fc <- forecast(boot_model, xreg = scenario_xreg)

dplyr::tibble(
  time = fc$time,
  baseline = as.numeric(fc$mean),
  scenario = as.numeric(scenario_fc$mean)
)
#> # A tibble: 2 × 3
#>   time       baseline scenario
#>   <date>        <dbl>    <dbl>
#> 1 2023-01-01    0.972     1.32
#> 2 2023-04-01    0.698     1.05

When a model contains stored bootstrap draws, forecast(..., xreg = ...) reuses the bootstrap refits and evaluates them on the scenario regressor path. That keeps the predictive uncertainty handling consistent between the baseline forecast and scenario forecasts.

Point Forecasts Only

If you are only interested in point estimates, leave se = FALSE. In that case, bootstrap is ignored and forecast() still returns the same object shape, with NA uncertainty fields.

point_model <- bridge(
  target = gdp_growth,
  indic = baro,
  indic_predict = "auto.arima",
  indic_aggregators = "mean",
  indic_lags = 1,
  target_lags = 1,
  h = 1,
  se = FALSE,
  bootstrap = list(type = "block", N = 20)
)

forecast(point_model)
#> Bridge forecast
#> -----------------------------------
#> Target series: gdp_growth
#> Forecast horizon: 1
#> Uncertainty: point forecast only
#> -----------------------------------
#>   time       mean 
#> 1 2023-01-01 0.972

Interpretation

These intervals are conditional on the aligned target-frequency design matrix. That means they are predictive intervals for the final target equation given the regressor path, rather than full end-to-end uncertainty for the whole mixed-frequency system.