I am trying to produce the Mean Absolute Scaled Error (MASE) for a custom time series model to compare its performance in forecasting several indicators with different units. I wanted to check my work by also calculating the MASE of the simple naive (one-step ahead) estimator or mean estimator both manually and with the Fable package. However I am stuck reproducing even the following simple example using the aus_production dataset from the tsibbledata package using the Fable package. I adapted the example from Hyndman & Athanasopoulos:


# This master dataset contains both the train and test sets
recent_production <- aus_production %>% 
  select(Quarter, Beer) %>%
  filter(year(Quarter) >= 1992)
# Training set
beer_train <- recent_production %>%
  filter(year(Quarter) <= 2007)

# Fit 2 models with training set
beer_fit <- beer_train %>%
    Mean = MEAN(Beer),
    `Naïve` = NAIVE(Beer)

# We see the training MAE of naive estimator from Fable is rounded to 55.1
# A tibble: 2 × 10
  .model .type          ME  RMSE   MAE    MPE  MAPE  MASE RMSSE   ACF1
  <chr>  <chr>       <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl>  <dbl>
1 Mean   Training 1.14e-14  43.9  35.6 -0.945  7.95  2.45  2.57 -0.120
2 Naïve  Training 8.14e- 1  65.9  55.1 -0.860 12.2   3.78  3.86 -0.244  

# Verify this with my manual training MAE
my_trainMAE <- beer_train %>%
  mutate(naive = lag(Beer,1),
         `abs naive error` = abs(Beer - naive)) %>%
  as.data.frame %>%
  summarise(mean(`abs naive error`, na.rm = TRUE)) %>%
[1] 55.08475

# Calculate MASE for the "mean" estimator manually
recent_production %>% 
  filter(Quarter == max(beer_train$Quarter)+1) %>%
  mutate(mean_forecast = mean(beer_train$Beer),
         `abs error for mean` = abs(Beer - mean_forecast),
         `MASE for mean` = mean(`abs error for mean`/my_trainMAE))
# A tsibble: 1 x 5 [1Q]
  Quarter  Beer mean_forecast `abs error for mean` `MASE for mean`
    <qtr> <dbl>         <dbl>                <dbl>           <dbl>
1 2007 Q1   427          436.                 9.45           0.172

# Let Fable calculate the out-of-sample one-step ahead forecast MASE
beer_fit %>% forecast(h = 1) %>% accuracy(recent_production)
# A tibble: 2 × 10
  .model .type     ME  RMSE   MAE    MPE  MAPE  MASE RMSSE  ACF1
  <chr>  <chr>  <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>
1 Mean   Test   -9.45  9.45  9.45  -2.21  2.21 0.649 0.554    NA
2 Naïve  Test  -64    64    64    -15.0  15.0  4.40  3.75     NA

# The warning message occurs because h=1 and is not related (to me knowledge)

I picked the "mean estimator" intentionally because it clearly depends on the entire history in the training set so the "shared" training set should be beer_train. First question is how does FABLE even calculate the MASE of the naive estimator on the training set different from 1. Then why can't I reproduce the naive training MAE that Fable uses to calculate the MASE (and the MASE as well)?


1 Answer 1


For quarterly data, the denominator in the MASE is based on seasonal naive forecasts, not naive forecasts. See https://otexts.com/fpp3/accuracy.html#scaled-errors for the definitions.


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