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Estimate a Mixed-Frequency Model

Source: R/bridge.R
mf_model.Rd

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

mf_model(
  target,
  indic,
  missing = "error",
  indic_predict = NULL,
  indic_aggregators = NULL,
  indic_lags = 0,
  target_lags = 0,
  h = 1,
  frequency_conversions = NULL,
  se = FALSE,
  bootstrap = NULL,
  full_system_bootstrap = FALSE,
  stationarity = "none",
  solver_options = NULL
)

bridge(...)

Arguments

target

A single target series in a tsbox::ts_boxable() format, such as a data frame or tibble with time and value/values columns, or a regular time-series object supported by tsbox.

indic

One or more indicator series in a tsbox::ts_boxable() format, such as data frames / tibbles with time and value/values columns, or regular time-series objects supported by tsbox.

missing

Character string controlling how explicit missing values in submitted target or indic series are handled. missing = "error" keeps the strict default and aborts on explicit missing values. missing = "drop" removes explicit missing values with a warning before downstream analysis, which is most useful when they correspond to supported ragged-edge gaps at the ends of series. missing = "impute" replaces explicit missing values by series-wise linear interpolation with endpoint carry before model fitting. Missing timestamps are always an error.

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), and "beta" uses (left_shape, right_shape) as the normalized beta shape parameters. 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 coefficient standard errors and prediction intervals should be computed. When TRUE, mf_model() reports HAC standard errors for the linear target equation, or Delta-HAC standard errors when parametric aggregation weights are estimated jointly.

bootstrap

A list of uncertainty controls. Currently only list(N = 100, block_length = NULL) is supported. N is the number of predictive simulation paths used when se = TRUE. If full_system_bootstrap = TRUE, the same N controls the number of full-system target-period block-bootstrap replications used for prediction intervals. block_length is only used by the full-system bootstrap. When block_length is NULL, mf_model() uses ceiling(n^(1/3)) based on the final target-period sample size.

full_system_bootstrap

Logical flag indicating whether prediction intervals and coefficient standard errors should be based on a full-system target-period block bootstrap instead of residual resampling and HAC / Delta-HAC uncertainty from the fitted target equation. This option is only used when se = TRUE. Because it refits the full bridge workflow on every draw, full_system_bootstrap = TRUE can be substantially slower than the default residual-resampling intervals.

stationarity

Character string controlling optional heuristic lower-order stationarity diagnostics. stationarity = "none" skips diagnostics. stationarity = "warn" checks submitted target and indicator series for a KPSS-style differencing signal and large variance shifts, and warns when those heuristics suggest that upstream transformations such as differences, growth rates, log changes, or demeaning may be appropriate.

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, warn to control whether non-convergence warnings are emitted, reltol for the relative convergence tolerance passed through to the selected optimizer backend, and start_values for user-supplied initial parameter values. Documented defaults are method = "L-BFGS-B", maxiter = 1000, n_starts = 5, trace = 0, warn = TRUE, and reltol = 1e-8. 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" and (left_shape, right_shape) for "beta". Named-list start_values must provide exactly the required number of values for each parametric indicator. Users can override reltol or suppress convergence warnings through solver_options = list(reltol = ..., warn = FALSE). These controls are ignored unless at least one indicator uses a parametric aggregator.

...

Arguments forwarded to mf_model().

Value

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

Details

Supported indicator forecasting methods are "mean", "last", "auto.arima", "ets", and "direct". Supported aggregation methods are "mean", "last", "sum", "unrestricted", "expalmon", "beta", 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", mf_model() 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, mf_model() 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.

Model specification

bridgr does not use a formula interface. Mixed-frequency bridge models are specified through separate target and indic series plus the forecasting, aggregation, and lag controls because the package must standardize, align, extend, and aggregate the time-series inputs before the final target regression formula can be assembled.

Terminology

Throughout bridgr, a target is the lower-frequency response series to be forecasted. An indicator is any higher-frequency predictor series aligned to the target frequency before the final regression is fit. Indicator forecasting refers to how end-of-sample indicator values are completed when the target horizon extends beyond the latest observed indicator block. Aggregation refers to how high-frequency indicator values within a target period are combined into bridge regressors. Direct prediction skips indicator forecasting and aligns the latest complete high-frequency blocks backward from the forecast horizon, while unrestricted aggregation keeps one separate coefficient per within-period high-frequency observation.

Input standardization

Submitted series are converted to a common internal table with id, time, and numeric values columns before model fitting. This means that additional input attributes beyond the series identifier, timestamps, and numeric values are not preserved in the fitted object unless they are re-encoded in those standardized columns.

Input assumptions

bridgr assumes that submitted target and indicator series are ordered by time within each series, free of duplicate timestamps and explicit missing values, and regular enough for the package to infer a supported target and indicator frequency. It also assumes that indicator series are at least as high-frequency as the target. Violations of these assumptions are rejected during preprocessing and validation rather than being silently repaired.

Stationarity

bridgr assumes that users provide target and indicator series on a scale that is appropriate for bridge-style forecasting. In practice this often means working with growth rates, differences, or other transformed series prepared upstream. This expectation primarily concerns the lower-order moments that matter most for bridge-style forecasting, typically the mean and variance of the submitted series. By default the package does not automatically enforce stationarity, but stationarity = "warn" enables heuristic pre-fit diagnostics for strong linear trends and variance shifts and points users toward differences, growth rates, log changes, demeaning, or other variance-stabilizing transformations when those heuristics are triggered.

Deprecated bridge() wrapper

bridge() is retained for compatibility and forwards to mf_model() with a deprecation warning.

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 <- tsbox::ts_pc(gdp)
#> [value]: 'values' 
#> [value]: 'values' 
gdp_growth <- tsbox::ts_na_omit(gdp_growth)
#> [value]: 'values' 
gdp_growth <- dplyr::slice_tail(gdp_growth, n = 12)
baro_small <- dplyr::slice_tail(baro, n = 36)

mf_model(
  target = gdp_growth,
  indic = baro_small,
  indic_predict = "auto.arima",
  indic_aggregators = "mean",
  indic_lags = 1,
  target_lags = 1,
  h = 1,
  frequency_conversions = c(mpq = 3),
  se = TRUE,
  bootstrap = list(N = 2),
  solver_options = list(seed = 123, n_starts = 1)
)
#> Mixed-frequency model summary
#> -----------------------------------
#> Target series: gdp_growth
#> Target frequency: quarter
#> Forecast horizon: 1
#> Estimation rows: 10
#> Regressors: baro_small, baro_small_lag1, gdp_growth_lag1
#> -----------------------------------
#> Target equation coefficients:
#>                 Estimate HAC SE
#> (Intercept)       -4.556  3.020
#> baro_small         0.118  0.025
#> baro_small_lag1   -0.061  0.042
#> gdp_growth_lag1   -0.188  0.136
#> -----------------------------------
#> Model fit:
#>  Statistic               Value
#>  R-squared               0.820
#>  Adjusted R-squared      0.730
#>  Residual standard error 1.093
#> -----------------------------------
#> Indicator summary:
#>            Frequency Predict    Aggregation
#> baro_small month     auto.arima mean       
#> -----------------------------------
#> Uncertainty:
#> Coefficient SEs: hac
#> Prediction intervals: residual resampling
#> Simulation paths: 2
#> -----------------------------------