fable::ARIMA() compared to forecast::auto.arima()

Different numbers of differences chosen, and excessive memory used.

library(fable)
#> Loading required package: fabletools
#> Registered S3 method overwritten by 'tsibble':
#>   method               from 
#>   as_tibble.grouped_df dplyr
library(forecast)
#> Registered S3 method overwritten by 'quantmod':
#>   method            from
#>   as.zoo.data.frame zoo
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union

# Different order of differences
auto.arima(AirPassengers, lambda = 0, biasadj = TRUE)
#> Series: AirPassengers 
#> ARIMA(0,1,1)(0,1,1)[12] 
#> Box Cox transformation: lambda= 0 
#> 
#> Coefficients:
#>           ma1     sma1
#>       -0.4018  -0.5569
#> s.e.   0.0896   0.0731
#> 
#> sigma^2 = 0.001371:  log likelihood = 244.7
#> AIC=-483.4   AICc=-483.21   BIC=-474.77
as_tsibble(AirPassengers) |>
  model(ARIMA(log(value))) |>
  report()
#> Series: value 
#> Model: ARIMA(2,0,0)(0,1,1)[12] w/ drift 
#> Transformation: log(value) 
#> 
#> Coefficients:
#>          ar1     ar2     sma1  constant
#>       0.5754  0.2614  -0.5553    0.0193
#> s.e.  0.0843  0.0842   0.0771    0.0015
#> 
#> sigma^2 estimated as 0.001323:  log likelihood=249.65
#> AIC=-489.29   AICc=-488.82   BIC=-474.88

# Benchmarks
bench::mark(
  forecast = auto.arima(AirPassengers, lambda = 0, biasadj = TRUE) |>
    forecast(h = 12),
  fable = as_tsibble(AirPassengers) |>
    model(ARIMA(log(value))) |>
    forecast(h = 12),
  check = FALSE
) |>
  select(expression, min, median, `itr/sec`, mem_alloc)
#> Warning: Some expressions had a GC in every iteration; so filtering is
#> disabled.
#> # A tibble: 2 × 5
#>   expression      min   median `itr/sec` mem_alloc
#>   <bch:expr> <bch:tm> <bch:tm>     <dbl> <bch:byt>
#> 1 forecast      1.59s    1.59s     0.628  398.74MB
#> 2 fable          5.5s     5.5s     0.182    1.27GB

^{Created on 2025-05-30 with reprex v2.1.1}

Reproduce the AirPassengers comparison using fable::ARIMA(log(value)) and forecast::auto.arima(), then inspect the ARIMA implementation and benchmark results to determine why differencing and memory use diverge. Done means the discrepancy is explained and, if confirmed as a bug, the behavior and memory use are corrected or covered by regression tests.