100 + 0.8·t + a yearly profile + noise (σ = 4). The textbook case: trend and seasonality.
Model to plot
Interval
Some models improve on the baseline (Seasonal naive): the best one, ARIMA(1,0,2)(1,1,1)[12], cuts its error by 58 %.
82 %measured interval coverage (you asked for 80 %)
4.27mean absolute error (MAE) of Holt-Winters
0.42MASE (< 1 = better than the naive forecast in-sample)
5.49σ estimated by the model (the seeded noise is 4.0)
Measured on 16 past origins (192 comparisons): the model is fitted using only what came before each origin, and we check whether what happened next fell inside the interval.
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Rolling-origin backtesting: the four models, same tests
| Model | MAE | MASE | MAPE | Coverage | Mean width | Versus baseline |
|---|---|---|---|---|---|---|
| Naive | 16.32 | 1.61 | 10.4 | 82 % | 59.5 | -65 % |
| Seasonal naivebaseline | 9.91 | 0.98 | 6.4 | 80 % | 29.5 | — |
| Holt-Winters | 4.27 | 0.42 | 2.8 | 82 % | 15.3 | 57 % |
| ARIMA(1,0,2)(1,1,1)[12] | 4.17 | 0.41 | 2.7 | 73 % | 13.1 | 58 % |
MAE and MASE: the lower, the better. Coverage: it should be close to the level you asked for (an 80 % interval that covers 60 % is a fake 80 %). "Versus baseline": how much less error than the better of the two naive forecasts (negative = worse). Click a row to plot that model.