Forecast the Simultaneous Equations Model (SEM)

This function produces forecasts for the SEM.

Usage

forecast(
  estimates,
  dates,
  ...,
  restrictions = NULL,
  options = list(approximate = FALSE, probs = NULL, fill = list(method = "mean"),
    conditional_innov_method = "projection")
)

# S3 method for class 'koma_estimate'
forecast(
  estimates,
  dates,
  ...,
  restrictions = NULL,
  options = list(approximate = FALSE, probs = NULL, fill = list(method = "mean"),
    conditional_innov_method = "projection")
)

Arguments

estimates

A koma_estimate object (estimate) containing the estimates for the simultaneous equations model, as well as a list of time series and a koma_seq object (system_of_equations) that were used in the estimation.

dates

Key-value list for date ranges in various model operations.

...

Additional parameters.

restrictions

List of model constraints. Default is empty.

options

Optional settings for forecasting. Use list(approximate = FALSE, probs = NULL, fill = list(method = "mean"), conditional_innov_method = "projection"). Elements:

• approximate: Logical. If FALSE (default), compute point forecasts from predictive draws. If TRUE, compute point forecasts from the mean/median of coefficient draws (fast approximation).

• probs: Numeric vector of quantile probabilities. If NULL, no quantiles are returned. When approximate = FALSE and probs is NULL, defaults to setdiff(get_quantiles(), 0.5).

• fill$method: "mean" or "median" used for conditional fill before forecasting.

• conditional_innov_method: Method for drawing conditional innovations. One of "projection" (default) or "eigen".

Value

An object of class koma_forecast.

An object of class koma_forecast is a list containing the following elements:

mean

Mean point forecasts as a list of time series of class koma_ts.

median

Median point forecasts as a list of time series of class koma_ts.

quantiles

A list of quantiles, where each element is named according to the quantile (e.g., "q_5", "q_50", "q_95"), and contains the forecasts for that quantile. This element is NULL if quantiles = FALSE.

ts_data

Time-series data set used in forecasting.

y_matrix

The Y matrix constructed from the balanced data up to the current quarter, used for forecasting.

x_matrix

The X matrix used for forecasting.

Details

The forecast function for SEM uses the estimates from the koma_estimate object to produce point forecasts and, optionally, quantile forecasts. When options$approximate is FALSE (default), point forecasts are computed from the predictive draws (with quantiles controlled by options$probs). When TRUE, point forecasts are computed from the mean and median of the coefficient draws for faster, approximate results.

The returned koma_forecast object keeps forecasts as named lists of koma_ts (for mean, median, and quantiles) alongside the input data and matrices used to produce them.

Use the print method to print a the forecast results, use the plot method, to visualize the forecasts and prediction intervals.

Parallel

This function provides the option for parallel computing through the future::plan() function. For a detailed example on executing estimate in parallel, see the vignette: vignette("parallel"). For more details, see the future package documentation.

See also

• For a comprehensive example of using forecast, see vignette("koma").

• Related functions within the package that may be of interest: estimate.

Examples

data("simulated_sem")

dates <- list(
  current = c(2024, 4),
  estimation = simulated_sem$dates$estimation,
  forecast = list(start = c(2025, 1), end = c(2025, 4))
)

ts_data <- simulated_sem$ts_data
# Endogenous series must stop at the last observed quarter before forecasting.
ts_data[simulated_sem$sys_eq$endogenous_variables] <- lapply(
  simulated_sem$sys_eq$endogenous_variables,
  function(x) {
    stats::window(ts_data[[x]], end = dates$current)
  }
)

set.seed(11)
fit <- estimate(
  ts_data = ts_data,
  sys_eq = simulated_sem$sys_eq,
  dates = dates,
  options = list(gibbs = list(ndraws = 10))
)
#> 
#> ── Gibbs Sampler Settings ──────────────────────────────────────────────────────
#> 
#> ── System Wide Settings ──
#> • Number of draws (`ndraws`): 10
#> • Burn-in ratio (`burnin_ratio`): 0.5
#> • Burn-in (`burnin`): 5
#> • Store frequency (`nstore`): 1
#> • Number of saved draws (`nsave`): 5
#> • Tau (`tau`): 1.1
#> 
#> 
#> ── Estimation ──────────────────────────────────────────────────────────────────
fc <- forecast(fit, dates = dates)
#> 
#> ── Forecast ────────────────────────────────────────────────────────────────────
print(fc)
#> <koma_ts>
#> attributes:
#>   series_type: list[9]
#>   method: list[9]
#>   value_type: list[9]
#>   anker: list[9]
#> 
#> series:
#>         consumption investment current_account manufacturing service     gdp
#> 2025 Q1      6.4738     4.5367          0.8352        0.5733 -0.3877 -0.0033
#> 2025 Q2      5.3499     4.2385          1.1044        0.4406 -0.1163  0.1064
#> 2025 Q3      5.4708     4.3407         -0.4310       -0.5032 -0.1463 -0.2890
#> 2025 Q4      5.1219     3.5070          2.4524        1.1098 -0.4564  0.1701
#>         real_interest_rate world_gdp population
#> 2025 Q1            -1.0418   -0.9163     0.9900
#> 2025 Q2            -0.3902    0.0282    -0.3553
#> 2025 Q3            -0.3920   -2.4366    -1.1260
#> 2025 Q4             0.2817    1.8674    -2.7807