Bridge Equation Nowcast

Estimate a bridge equation via OLS and produce a nowcast for the current or specified period. Bridge equations translate higher-frequency indicators (e.g. monthly) into estimates of a lower-frequency target (e.g. quarterly GDP). Following standard central bank practice (Baffigi et al. 2004, Runstler and Sedillot 2003), an autoregressive term for the target variable can be included via the ar_order argument.

Usage

nc_bridge(formula, data, newdata = NULL, ar_order = 1L, alpha = 0.05)

Arguments

formula

A formula with the target variable on the left-hand side and indicator variables on the right (e.g. target ~ ind1 + ind2).

data

A data frame (or nc_dataset) containing the variables in formula plus a date column.

newdata

A one-row data frame with indicator values for the nowcast period. If NULL, the last complete row of data is used.

ar_order

Integer. Number of autoregressive lags of the target to include (default 1). Set to 0 for a static bridge equation with no AR terms.

alpha

Numeric. Significance level for prediction intervals (default 0.05).

Value

A nowcast_result object.

Details

Prediction intervals are computed using the full prediction standard error, which accounts for both residual variance and estimation uncertainty in the coefficients, evaluated against a t distribution with appropriate degrees of freedom.

When ar_order > 0, the model includes a lagged dependent variable. The reported standard errors assume homoskedastic, serially uncorrelated errors. If residuals exhibit autocorrelation (indicated by the Durbin-Watson statistic in details$dw_stat), consider extracting the fitted model via result$model and applying HAC standard errors from the sandwich package.

References

Baffigi, A., Golinelli, R. and Parigi, G. (2004). Bridge models to forecast the euro area GDP. International Journal of Forecasting, 20(3), 447–460.

Examples

# \donttest{
# Synthetic example
set.seed(42)
d <- data.frame(
  date = as.Date(paste0(2015:2024, "-01-01")),
  gdp = cumsum(rnorm(10, 0.5, 0.3)),
  ind1 = cumsum(rnorm(10, 0.4, 0.2)),
  ind2 = cumsum(rnorm(10, 0.3, 0.4))
)
nc_bridge(gdp ~ ind1 + ind2, data = d)
#> ℹ Durbin-Watson = 2.884 suggests residual autocorrelation.
#> ℹ OLS standard errors may be unreliable. Consider HAC SEs via sandwich.
#> 
#> ── Nowcast (Bridge Equation) ───────────────────────────────────────────────────
#> • Nowcast: 6.7919
#> • SE: 0.3325
#> • "95%" CI: [5.9373, 7.6466]
#> • Target period: 2024-01-01
#> • R-squared: 0.9877 | Obs: 9
# }