How to find the mu and sigma associated with an snaive fit

[alexhallam]

I would like to know the mu and sigma that was estimated and also the mu and sigma in the forecast horizon given a snaive fit.

library(fable)
library(tsibble)
library(tsibbledata)
library(lubridate)
library(dplyr)
aus_retail %>%
  filter(
    State %in% c("New South Wales", "Victoria"),
    Industry == "Department stores"
  ) %>% 
  model(
    snaive = SNAIVE(Turnover)
  ) |>
  glance()

# A tibble: 2 × 4
  State           Industry          .model sigma2
  <chr>           <chr>             <chr>   <dbl>
1 New South Wales Department stores snaive   492.
2 Victoria        Department stores snaive   237.

I currently see sigma2, but I am not sure what that is referring to. If I calculated backward looking var I get

aus_retail %>%
  as_tibble() |>
  filter(
    State %in% c("New South Wales", "Victoria"),
    Industry == "Department stores"
  ) %>% 
  group_by(State) |>
  summarise(sigma2 = sd(Turnover))

  State           sigma2
  <chr>            <dbl>
1 New South Wales 23111.
2 Victoria        14336.

The sigma2 and var are not matching so I probably do not understand what is going on.

[mitchelloharawild]

sigma2 in the glance() output is the variance of the innovation residuals.

library(fable)
library(tsibble)
library(tsibbledata)
library(lubridate)
library(dplyr)
aus_retail %>%
  filter(
    State %in% c("New South Wales", "Victoria"),
    Industry == "Department stores"
  ) %>% 
  model(
    snaive = SNAIVE(Turnover)
  ) |>
  augment() |> 
  as_tibble() |> 
  group_by(State) |> 
  summarise(sigma2 = var(.innov, na.rm = TRUE))
#> # A tibble: 2 x 2
#>   State           sigma2
#>   <chr>            <dbl>
#> 1 New South Wales   492.
#> 2 Victoria          237.

The forecast distribution parameters can be obtained using distributional::parameters():

aus_retail %>%
  filter(
    State %in% c("New South Wales", "Victoria"),
    Industry == "Department stores"
  ) %>% 
  model(
    snaive = SNAIVE(Turnover)
  ) |>
  forecast() |> 
  mutate(distributional::parameters(Turnover))
#> # A fable: 48 x 8 [1M]
#> # Key:     State, Industry, .model [2]
#>    State           Industry        .model    Month    Turnover .mean    mu sigma
#>    <chr>           <chr>           <chr>     <mth>      <dist> <dbl> <dbl> <dbl>
#>  1 New South Wales Department sto~ snaive 2019 Jan N(452, 570)  452.  452.  23.9
#>  2 New South Wales Department sto~ snaive 2019 Feb N(350, 570)  350.  350.  23.9
#>  3 New South Wales Department sto~ snaive 2019 Mar N(457, 570)  457   457   23.9
#>  4 New South Wales Department sto~ snaive 2019 Apr N(454, 570)  454.  454.  23.9
#>  5 New South Wales Department sto~ snaive 2019 May N(502, 570)  502.  502.  23.9
#>  6 New South Wales Department sto~ snaive 2019 Jun N(531, 570)  531.  531.  23.9
#>  7 New South Wales Department sto~ snaive 2019 Jul N(446, 570)  446.  446.  23.9
#>  8 New South Wales Department sto~ snaive 2019 Aug N(429, 570)  429.  429.  23.9
#>  9 New South Wales Department sto~ snaive 2019 Sep N(462, 570)  462.  462.  23.9
#> 10 New South Wales Department sto~ snaive 2019 Oct N(503, 570)  503.  503.  23.9
#> # i 38 more rows

Similar can be done for the fitted values, obtained with the fitted() function.

^{Created on 2023-07-07 with reprex v2.0.2}