Estimate a Bridge Model — bridge • bridgr

Estimate a bridge model that links one lower-frequency target series to one or more higher-frequency indicator series. Indicators are aligned to the target frequency by forecasting any missing higher-frequency observations and aggregating them within each target period.

Usage

bridge(
  target,
  indic,
  indic_predict = NULL,
  indic_aggregators = NULL,
  indic_lags = 0,
  target_lags = 0,
  h = 1,
  frequency_conversions = NULL,
  se = FALSE,
  bootstrap = NULL,
  solver_options = NULL,
  ...
)

Arguments

target: A single target series in a tsbox::ts_boxable() format.
indic: One or more indicator series in a tsbox::ts_boxable() format.
indic_predict: A character vector of indicator forecasting methods. Length must be 1 or equal to the number of indicator series. Setting indic_predict = "direct" switches to direct MIDAS-style alignment: the indicators are not forecasted, and the most recent complete high-frequency blocks are assigned backward to the target periods. Direct alignment must be used for all indicators at once. When h > 1, the latest complete block is assigned to the farthest requested forecast horizon and earlier complete blocks are assigned backward from there. For indic_predict = "mean", missing high-frequency observations are filled with the mean of the latest available obs_per_target high-frequency observations, and that same mean is extended across the forecast horizon.
indic_aggregators: A character vector of aggregation methods or a list of numeric weights. Length must be 1 or equal to the number of indicator series. Numeric weights must sum to one and have the appropriate length for the inferred target-period block size. "unrestricted" keeps one separate coefficient per high-frequency observation within the target period. The parametric aggregators use two coefficients each: "expalmon" uses (linear, quadratic), "beta" uses (left_shape, right_shape) as the normalized beta shape parameters, and "legendre" uses (first_order, second_order) as coefficients on the first two shifted orthonormal Legendre basis functions. When indic_predict = "direct", indic_aggregators is ignored and direct blocks are averaged within each target period.
indic_lags: A non-negative integer giving the number of target-period lags to add for each aggregated indicator.
target_lags: A non-negative integer giving the autoregressive order in the target equation.
h: A positive integer forecast horizon measured in target periods.
frequency_conversions: A named numeric vector used to customize the regular frequency ladder. Supported names are spm, mph, hpd, dpw, wpm, mpq, and qpy.
se: Logical flag indicating whether bootstrap coefficient standard errors and predictive forecast intervals should be computed. When FALSE, bootstrap is ignored.
bootstrap: A list of bootstrap controls. Currently only list(type = "block", N = 100, block_length = NULL) is supported. type must be "block", N is the number of bootstrap replications, and block_length is the target-frequency block length. When block_length is NULL, bridge() uses ceiling(n^(1/3)) based on the final target-period estimation sample size. The bootstrap is conditional on the aligned low-frequency design matrix and therefore does not re-estimate indicator forecasts or aggregation weights, but the stored forecast draws include simulated future target shocks so forecast() returns predictive intervals.
solver_options: A list of optional controls for joint parametric-weight optimization. Supported entries are: method for the optimizer ("L-BFGS-B", "BFGS", "Nelder-Mead", or "nlminb"), maxiter for the iteration budget per optimization run, n_starts for the number of multi-start attempts, seed for reproducible random restarts, trace for optimizer verbosity, and start_values for user-supplied initial parameter values. start_values can be either a numeric vector or a named list. For a numeric vector, values are concatenated in indicator order across the parametric aggregators. Within each indicator, the parameter order is (linear, quadratic) for "expalmon", (left_shape, right_shape) for "beta", and (first_order, second_order) for "legendre". Named-list start_values must provide exactly the required number of values for each parametric indicator. These controls are ignored unless at least one indicator uses a parametric aggregator.
...: Reserved for future extensions.

Value

An object of class "bridge" containing the standardized input series, inferred frequencies, aligned estimation and forecast datasets, the fitted target model, fitted indicator models, and metadata required by forecast.bridge() and summary.bridge().

Details

Supported indicator forecasting methods are "mean", "last", "auto.arima", "ets", and "direct". Supported aggregation methods are "mean", "last", "sum", "unrestricted", "expalmon", "beta", "legendre", or a numeric weight vector supplied inside a list(). "unrestricted" expands each high-frequency observation within a target period into its own bridge regressor, which corresponds to a U-MIDAS style specification when the frequency gap is small. When one or more indicators use a parametric aggregator, the corresponding aggregation weights are estimated jointly against the final bridge-model objective rather than one indicator at a time.

Unrestricted mixed-frequency regressions can become parameter-heavy quickly. When indic_aggregators = "unrestricted", bridge() warns if the final estimation sample contains fewer than 10 observations per predictor in the bridge regression.

The package assumes a regular frequency ladder second -> minute -> hour -> day -> week -> month -> quarter -> year. The default number of lower-level observations per higher-level unit is:

spm = 60
mph = 60
hpd = 24
dpw = 7
wpm = 4
mpq = 3
qpy = 4

Users can override any subset of these values with frequency_conversions. If a target period contains more high-frequency observations than implied by the current mapping, bridge() keeps the most recent observations and emits a summarized warning. If a target period contains fewer observations than required, the call fails. Month-, quarter-, and year-based input dates are standardized to period starts when needed for frequency recognition.

References

Baffigi, A., Golinelli, R., & Parigi, G. (2004). Bridge models to forecast the euro area GDP. International Journal of Forecasting, 20(3), 447-460. doi:10.1016/S0169-2070(03)00067-0

Ghysels, E., Sinko, A., & Valkanov, R. (2007). MIDAS regressions: Further results and new directions. Econometric Reviews, 26(1), 53-90. doi:10.1080/07474930600972467

Andreou, E., Ghysels, E., & Kourtellos, A. (2010). Regression models with mixed sampling frequencies. Journal of Econometrics, 158(2), 246-261. doi:10.1016/j.jeconom.2010.01.004

Schumacher, C. (2016). A comparison of MIDAS and bridge equations. International Journal of Forecasting, 32(2), 257-270. doi:10.1016/j.ijforecast.2015.07.004

Burri, M. (2026). Nowcasting Swiss GDP Growth From Public Lead Texts: Simple Methods Are Sufficient. Oxford Bulletin of Economics and Statistics, 1-25. doi:10.1111/obes.70073

Examples

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

model <- bridge(
  target = gdp_growth,
  indic = baro,
  indic_predict = "auto.arima",
  indic_aggregators = "mean",
  indic_lags = 1,
  target_lags = 1,
  h = 2
)

expalmon_model <- bridge(
  target = gdp_growth,
  indic = baro,
  indic_predict = "auto.arima",
  indic_aggregators = "expalmon",
  solver_options = list(seed = 123, n_starts = 3),
  h = 1
)

forecast(model)
#> Bridge forecast
#> -----------------------------------
#> Target series: gdp_growth
#> Forecast horizon: 2
#> Uncertainty: point forecast only
#> -----------------------------------
#>   time       mean 
#> 1 2023-01-01 0.972
#> 2 2023-04-01 0.698
summary(expalmon_model)
#> Bridge model summary
#> -----------------------------------
#> Target series: gdp_growth
#> Target frequency: quarter
#> Forecast horizon: 1
#> Estimation rows: 75
#> Regressors: baro
#> -----------------------------------
#> Target equation coefficients:
#>             Estimate
#> (Intercept)   -9.371
#> baro           0.098
#> -----------------------------------
#> Indicator summary:
#>      Frequency Predict    Aggregation
#> baro month     auto.arima expalmon   
#> -----------------------------------
#> Estimated parametric aggregation:
#> baro weights: 0.006, 0.994, 0.000
#> baro parameters: -4.914, -10.000
#> -----------------------------------
#> Joint parametric aggregation optimization:
#> Method: L-BFGS-B
#> Objective value: 60.832
#> Convergence code: 0
#> Best start: 1 / 3
#> -----------------------------------