Some forecasting applications require having a continuous vector of the forecasted variable. This vector needs to combine observed and forecasted values. One such need is to produce estimations of multi-period (e.g. annual) growth rates based on one-period forecasts.

The reprex below illustrates how this can be done for the particular example of tsibble::tourism data. I also made an example on rpubs which illustrates using the combined fable for differencing with a lag.

• To properly calculate growth rates later, I need the response variable to be log-transformed.
• In the data from augment() I am replacing observed values with a zero-variance distribution: dist_lognormal( log(Trips), 0)) . I fix the tsibble to be of class fable.
• Unfortunately forecast() by default returns a fable with a dist_transformed. dist_transformed has no methods to calculate differences between distributions. I decided to replace them with dist_lognormal distributions.
• I combined both fables.

Those steps took me over a week to develop and are not obvious to a beginner and there is no vignette for that. I had to dig into aspects of distributional and vctrs packages to use the proper functions to get the data out.

Conclusion: There is a need for a function that produces output like a combined output of augment() and forecast(). Maybe functions for the proper calculation of multi-period growth rates could be added too.

library(tsibble)
library(dplyr)
library(fable)
library(vctrs)
library(distributional)

tsb_selected <- tourism |>
  filter(Region %in% c('Adelaide') )  |>
  filter(Purpose %in% c('Business', 'Holiday')  )

fit_selected <- tsb_selected        |>
  model( ets = ETS(log(Trips) ) )

fc_ahead <-  fit_selected |>
  forecast(h = 5)

fc_ahead |>
  group_by_key() |>
  slice_tail(n=3) |>
  knitr::kable()

fable_from_augmented_fit <- fit_selected |>
  augment()  |>
  select(-any_of(c(".innov", ".fitted", ".resid"))) |>
  mutate(Trips =  dist_lognormal(  log(Trips), 0))  |>
  mutate(.mean = mean(Trips))

dimnames(fable_from_augmented_fit$Trips) <- "Trips"

fable_from_augmented_fit <- fable_from_augmented_fit |>
  as_fable(response = "Trips", distribution = "Trips")

fable_from_augmented_fit |>
  group_by_key() |>
  slice_tail(n=3) |>
  knitr::kable()

y_as_lnorm <- fc_ahead |>
  pull(Trips)  |>
  vec_data()  |>
  lapply (\(x)  x[[1]] )   |>
  vec_restore( fc_ahead$Trips )    |>
  exp()

fc_as_lnorm <- fc_ahead  |>
  mutate( Trips = y_as_lnorm ) |>
  mutate( .mean = mean(Trips) )

fc_all <- dplyr::bind_rows(fable_from_augmented_fit, fc_as_lnorm)

autoplot(fc_all, level=90)  |> print()

fc_all |>
  group_by_key() |>
  slice_tail(n=3) |>
  knitr::kable()

^{Created on 2025-12-21 with reprex v2.1.1}