transform_forecast: Transform forecasts from model scale to data scale by...

In doBy: Groupwise Statistics, LSmeans, Linear Estimates, Utilities

Transform forecasts from model scale to data scale by simulation

Description

transform_forecast() takes a univariate time series forecast fitted on a transformed (model) scale and produces a new forecast object on the original data scale. This is done by simulating future paths on the model scale, transforming each path with a user-supplied function, and then computing pointwise means and prediction intervals on the transformed scale.

Usage

transform_forecast(fc_object, trans_fun, nsim = 2000L, level = 95, y0 = 1)

Arguments

fc_object	A "forecast" object (from the forecast package) for a univariate time series, typically obtained via forecast::forecast().
trans_fun	A function of the form function(x, y0) ... that takes a numeric vector x on the model scale and a scalar starting value y0 on the output scale and returns a numeric vector of the same length on the output scale.
nsim	Integer; number of simulated future paths to use. Larger values give smoother prediction intervals but take longer to compute.
level	Numeric; prediction interval coverage in percent.
y0	Numeric; starting value on the output scale used to reconstruct the historical series from fc_object$x. For percentage change models it is often natural to set y0 = 1 and interpret the resulting series as an index.

Details

The function assumes that fc_object is a "forecast" object as produced by the forecast package, and that fc_object$model supports simulate() with arguments nsim and future.

The transformation function trans_fun must have the form trans_fun(x, y0), where x is a numeric vector representing a path on the model scale (for example log-values or percentage changes), and y0 is a scalar "starting value" on the output scale. The function must return a numeric vector of the same length as x giving the corresponding path on the output scale.

Internally, transform_forecast() first reconstructs a historical series on the output scale by applying trans_fun() to fc_object$x with the supplied y0. It then simulates nsim future paths from fc_object$model on the model scale, transforms each path to the output scale using trans_fun() with y0 equal to the last value of the reconstructed historical series, and finally computes the pointwise mean and prediction intervals (of nominal coverage level) across the simulated paths. The result is returned as a new "forecast" object with x, mean, lower, and upper on the output scale.

Value

A "forecast" object similar to fc_object, but with the components x, mean, lower, and upper defined on the output (data) scale.

See Also

forecast, auto.arima, simulate, ts.

Examples

## Example 1: Log-transform of the Canadian lynx data
if (requireNamespace("forecast", quietly = TRUE)) {

  llynx   <- log(lynx)
  fit_log <- forecast::auto.arima(llynx)
  fc_log  <- forecast::forecast(fit_log, h = 20)
  forecast::autoplot(fc_log)
  ## transformation: log -> original scale
  trans_log <- function(z, y0) {
    exp(z)
  }
  fc_lynx <- transform_forecast(fc_log, trans_fun = trans_log,
                            nsim = 20, level = 95, y0 = 1)
  plot(fc_lynx)
  forecast::autoplot(fc_lynx) + ggplot2::theme_minimal()
}


## Not run: 
if (requireNamespace("forecast", quietly = TRUE)) {
## Example 2 (variation): CO2 series, log-transform
  lco2    <- log(co2)
  fit_co2 <- forecast::auto.arima(lco2)
  fc_log_co2 <- forecast::forecast(fit_co2, h = 24)
  forecast::autoplot(fc_log_co2)
  trans_log <- function(z, y0) exp(z)

  fc_co2 <- transform_forecast(fc_log_co2, trans_fun = trans_log,
                           nsim = 20, level = 95, y0 = 1)
  forecast::autoplot(fc_co2) + ggplot2::theme_minimal()
}

# ## Example 3: Percentage change in income (uschange$Income)
if (requireNamespace("forecast", quietly = TRUE) &&
    requireNamespace("fpp2", quietly = TRUE)) {
  income <- uschange[, "Income"]  # quarterly percentage changes (%)

  ## transformation: pct change -> index with base 1
  trans_pct <- function(r, y0) {
    y0 * cumprod(1 + r / 100)
  }

  fit_pct <- forecast::auto.arima(income)
  fc_pct  <- forecast::forecast(fit_pct, h = 24)
  forecast::autoplot(fc_pct)
  fc_idx  <- transform_forecast(fc_pct, trans_fun = trans_pct,
                            nsim = 200, level = 95, y0 = 1)

  plot(fc_idx)
  forecast::autoplot(fc_idx) + ggplot2::theme_minimal()
 }
 
## End(Not run)
 

doBy documentation built on Dec. 2, 2025, 9:08 a.m.