What does it mean when ARIMA's final forecast errors have low variance?

When the final forecast errors of an ARIMA model have low variance, it indicates that the model is providing predictions that are consistently close to the actual outcomes. This means that the model has effectively captured the underlying patterns in the historical data it was trained on, and thus aligns well with past data.

Low variance in forecast errors suggests that the model's predictions are stable and reliable, demonstrating that the chosen parameters and structure of the ARIMA model are appropriate for the time series being analyzed. This consistency in the model's error suggests it is well-tuned to the data rather than being influenced by noise or random fluctuations, confirming that the model's assumptions and fitting process were successful in extracting the relevant patterns from the historical data.