Principles of forecasting: How to obtain the boostraped samples

[nickcox896]

In section 5.5 (third edition) we have
fc <- fit |> forecast(h = 30, bootstrap = TRUE)
fc
#> # A fable: 30 x 5 [1]
#> # Key: Symbol, .model [1]
#> Symbol .model day Close .mean
#>
#> 1 GOOG NAIVE(Close) 253 sample[5000] 759.
#> 2 GOOG NAIVE(Close) 254 sample[5000] 759.
#> 3 GOOG NAIVE(Close) 255 sample[5000] 758.
#> 4 GOOG NAIVE(Close) 256 sample[5000] 759.
#> 5 GOOG NAIVE(Close) 257 sample[5000] 759.
#> 6 GOOG NAIVE(Close) 258 sample[5000] 759.
#> 7 GOOG NAIVE(Close) 259 sample[5000] 759.
#> 8 GOOG NAIVE(Close) 260 sample[5000] 759.
#> 9 GOOG NAIVE(Close) 261 sample[5000] 759.
#> 10 GOOG NAIVE(Close) 262 sample[5000] 759.
#> # ℹ 20 more rows

How can I see the (5000) bootstraped values for each forecasting period so that I can extract them as a data frame (where the columns will be the number of simulations and the rows will be the forecast dates)?

[mitchelloharawild]

library(fpp3)
#> ── Attaching packages ──────────────────────────────────────────── fpp3 1.0.3 ──
#> ✔ tibble      3.3.1          ✔ tsibble     1.2.0.9000
#> ✔ dplyr       1.2.0          ✔ tsibbledata 0.4.1     
#> ✔ tidyr       1.3.2          ✔ ggtime      0.2.0.9000
#> ✔ lubridate   1.9.5          ✔ feasts      0.5.0     
#> ✔ ggplot2     4.0.2          ✔ 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()
fit <- gafa_stock |> 
  filter(Symbol == "GOOG") |> 
  mutate(t = seq_along(Date)) |> 
  as_tsibble(index = t, regular = TRUE) |> 
  model(NAIVE(Close))

The simplest way is to instead use generate(), which returns the samples and replicate identifier (.rep) directly.

fc_sim <- fit |> 
  generate(h = 30, bootstrap = TRUE)
fc_sim
#> # A tsibble: 30 x 5 [1]
#> # Key:       Symbol, .model, .rep [1]
#>    Symbol .model           t .rep   .sim
#>    <chr>  <chr>        <dbl> <chr> <dbl>
#>  1 GOOG   NAIVE(Close)  1259 1     1051.
#>  2 GOOG   NAIVE(Close)  1260 1     1041.
#>  3 GOOG   NAIVE(Close)  1261 1     1029.
#>  4 GOOG   NAIVE(Close)  1262 1     1027.
#>  5 GOOG   NAIVE(Close)  1263 1     1032.
#>  6 GOOG   NAIVE(Close)  1264 1     1029.
#>  7 GOOG   NAIVE(Close)  1265 1     1028.
#>  8 GOOG   NAIVE(Close)  1266 1     1036.
#>  9 GOOG   NAIVE(Close)  1267 1     1026.
#> 10 GOOG   NAIVE(Close)  1268 1     1042.
#> # ℹ 20 more rows

Alternatively, you can use distributional::parameters() to obtain the parameters of the distribution.
For a dist_sample() distribution, this returns a list of the samples which can be unnested.

fc <- fit |> 
  forecast(h = 30, bootstrap = TRUE)
fc
#> # A fable: 30 x 5 [1]
#> # Key:     Symbol, .model [1]
#>    Symbol .model           t        Close .mean
#>    <chr>  <chr>        <dbl>       <dist> <dbl>
#>  1 GOOG   NAIVE(Close)  1259 sample[5000] 1036.
#>  2 GOOG   NAIVE(Close)  1260 sample[5000] 1036.
#>  3 GOOG   NAIVE(Close)  1261 sample[5000] 1036.
#>  4 GOOG   NAIVE(Close)  1262 sample[5000] 1036.
#>  5 GOOG   NAIVE(Close)  1263 sample[5000] 1036.
#>  6 GOOG   NAIVE(Close)  1264 sample[5000] 1036.
#>  7 GOOG   NAIVE(Close)  1265 sample[5000] 1036.
#>  8 GOOG   NAIVE(Close)  1266 sample[5000] 1036.
#>  9 GOOG   NAIVE(Close)  1267 sample[5000] 1036.
#> 10 GOOG   NAIVE(Close)  1268 sample[5000] 1036.
#> # ℹ 20 more rows

fc |> 
  as_tibble() |> 
  mutate(
    # Extract the samples from the distribution
    distributional::parameters(Close), 
    # Add an identifier for each replicate
    .rep = list(seq_len(5000L))
  ) |> 
  # Unnest the list columns into a flat tibble
  unnest(c(x, .rep))
#> # A tibble: 150,000 × 7
#>    Symbol .model           t        Close .mean     x  .rep
#>    <chr>  <chr>        <dbl>       <dist> <dbl> <dbl> <int>
#>  1 GOOG   NAIVE(Close)  1259 sample[5000] 1036. 1043.     1
#>  2 GOOG   NAIVE(Close)  1259 sample[5000] 1036. 1044.     2
#>  3 GOOG   NAIVE(Close)  1259 sample[5000] 1036. 1035.     3
#>  4 GOOG   NAIVE(Close)  1259 sample[5000] 1036. 1041.     4
#>  5 GOOG   NAIVE(Close)  1259 sample[5000] 1036. 1035.     5
#>  6 GOOG   NAIVE(Close)  1259 sample[5000] 1036. 1048.     6
#>  7 GOOG   NAIVE(Close)  1259 sample[5000] 1036. 1045.     7
#>  8 GOOG   NAIVE(Close)  1259 sample[5000] 1036. 1037.     8
#>  9 GOOG   NAIVE(Close)  1259 sample[5000] 1036. 1023.     9
#> 10 GOOG   NAIVE(Close)  1259 sample[5000] 1036. 1032.    10
#> # ℹ 149,990 more rows

^{Created on 2026-03-02 with reprex v2.1.1}

[nickcox896]

Many thanks!!