calculating aggregate percentiles

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I have a flow variable (quarterly GPD).

And I want to make annual forecasts; in particular, I want to predict the next 8 years (4*8=32 quarters ahead)

I generate 1000 paths for each horizon-quarter.
So for each of the 32 horizon-quarters, I get 1000 values.

My goal is to calculate the quantiles annually; that is for each of the 8 years.

Should I add up the 1000 values by year before calculating the annual quantiles?

I display a hypothetical example from your nice book but I am not sure if my code below is correct

library(fpp3)
recent_production <- aus_production |> filter(year(Quarter) >= 1992)
beer_fit <- recent_production  |> model(ARIMA(Beer))
beer_fc <- beer_fit  %>%  generate(times = 1000, h = 32)  %>%
 as_tibble() |>
  group_by(.rep) |>
  summarise(.sim = sum(.sim))

I am not sure how to proceed after this code

[robjhyndman]

First, your group_by needs to include the year, so your sums are annual. You also need to consider whether all four quarters are available in each year.

library(fpp3)
#> ── Attaching packages ──────────────────────────────────────────── fpp3 1.0.3 ──
#> ✔ tibble      3.3.1     ✔ tsibble     1.2.0
#> ✔ dplyr       1.2.1     ✔ tsibbledata 0.4.1
#> ✔ tidyr       1.3.2     ✔ ggtime      0.2.0
#> ✔ lubridate   1.9.5     ✔ feasts      0.5.0
#> ✔ ggplot2     4.0.3     ✔ fable       0.5.0
#> ── Conflicts ───────────────────────────────────────────────── fpp3_conflicts ──
#> ✖ lubridate::date()    masks base::date()
#> ✖ dplyr::filter()      masks stats::filter()
#> ✖ tsibble::intersect() masks base::intersect()
#> ✖ tsibble::interval()  masks lubridate::interval()
#> ✖ dplyr::lag()         masks stats::lag()
#> ✖ tsibble::setdiff()   masks base::setdiff()
#> ✖ tsibble::union()     masks base::union()
recent_production <- aus_production |> filter(year(Quarter) >= 1992)
beer_fit <- recent_production |> model(ARIMA(Beer))
# Generate future sample paths
beer_fc <- beer_fit |>
  generate(times = 1000, h = 32)
# Aggregate to annual for complete years
beer_fc <- beer_fc |>
  as_tibble() |>
  mutate(year = year(Quarter)) |>
  group_by(.rep, year) |>
  summarise(
    nquarters = n(),
    .sim = sum(.sim),
    .groups = "drop"
  ) |>
  filter(nquarters == 4L) |>
  select(-nquarters)

Next you need to convert the simulated values into a distributional object, so you can create a fable:

# Convert to fable
beer_fc <- beer_fc |>
  group_by(year) |>
  summarise(Beer = distributional::dist_sample(list(.sim))) |>
  as_fable(index = year, response = "Beer", distribution = Beer)

Here is the result, plotted with the historical data. Again, only complete years are used.

beer_fc |>
  autoplot(
    recent_production |>
      as_tibble() |>
      mutate(year = year(Quarter)) |>
      group_by(year) |>
      summarise(nquarters = n(), Beer = sum(Beer)) |>
      filter(nquarters == 4L) |>
      as_tsibble(index = year)
  )

^{Created on 2026-06-26 with reprex v2.1.1}

[newsagent]

Thanks a lot!