ARIMA forecasts don't work for x weekly, monthly and quarterly data where x > 1

[bottervanger]

See reprex below.

The calculation of fc_start seems to be wrong.

fc_start <- object$tsp$range[2]+round(as.numeric(diff(object$tsp$range)+1)/nrow(object$est), 6)

From what I can tell it's doing:
fc_start <- <last index value> + (<time diff between start and end> + 1 ) / <no of samples>
while it should be:
fc_start <- <last index value> + <time diff between start and end> / <no of intervals>
or, equivalently:
fc_start <- <last index value> + <time diff between start and end> / (<no of samples> - 1)

data <- tsibble::tsibble(
    week = (lubridate::today() + lubridate::period(weeks = seq(1, 9, 4))) |>
        tsibble::yearweek(),
    number = 1:3,
    index = week
)
data |>
    fabletools::model(arima = fable::ARIMA(number ~ pdq() + PDQ())) |>
    fabletools::forecast(h = 1)
#> Error in `mutate()`:
#> ! Problem while computing `arima = (function (object, ...) ...`.
#> Caused by error in `forecast()`:
#> ! Forecasts from an ARIMA model must start one step beyond the end of the trained data.

#> Backtrace:
#>      ▆
#>   1. ├─fabletools::forecast(...)
#>   2. ├─fabletools:::forecast.mdl_df(...)
#>   3. │ └─dplyr::mutate_at(...)
#>   4. │   ├─dplyr::mutate(.tbl, !!!funs)
#>   5. │   └─dplyr:::mutate.data.frame(.tbl, !!!funs)
#>   6. │     └─dplyr:::mutate_cols(.data, dplyr_quosures(...), caller_env = caller_env())
#>   7. │       ├─base::withCallingHandlers(...)
#>   8. │       └─mask$eval_all_mutate(quo)
#>   9. ├─fabletools (local) `<fn>`(...)
#>  10. └─fabletools:::forecast.lst_mdl(...)
#>  11.   └─fabletools:::mapply_maybe_parallel(...)
#>  12.     └─base::mapply(FUN = .f, ..., MoreArgs = MoreArgs, SIMPLIFY = SIMPLIFY)
#>  13.       ├─fabletools (local) `<fn>`(dots[[1L]][[1L]], dots[[2L]][[1L]], h = 1, point_forecast = `<named list>`)
#>  14.       └─fabletools:::forecast.mdl_ts(...)
#>  15.         ├─fabletools::forecast(...)
#>  16.         └─fable:::forecast.ARIMA(object$fit, new_data, specials = specials, times = times, ...)
#>  17.           └─rlang::abort("Forecasts from an ARIMA model must start one step beyond the end of the trained data.")

^{Created on 2023-04-13 with reprex v2.0.2}

Edit: wrap text in code to prevent angle brackets being swallowed
Edit: add missing term to calculation interpretation

[bottervanger]

The calculation of fc_start seems to work if you use an interval of single weeks, months, quarters, but not for anything else.