What is sMAPE and what are its problems?

sMAPE (Symmetric Mean Absolute Percentage Error) is a metric for evaluating forecast accuracy, especially in time series tasks. It is calculated as the average across all points:

[ sMAPE = \frac{100%}{n} \sum_{t=1}^n \frac{|F_t - A_t|}{(|A_t| + |F_t|)/2} ]

where (F_t) is the forecast, (A_t) is the actual value.

Advantages of sMAPE:

• Normalizes the error, making it relative and symmetric with respect to the forecast and actual value.
• Avoids division by zero, as the denominator is the sum of absolute values.

Problems of sMAPE:

• When actual and forecast values are very small, the denominator approaches zero, which can lead to large errors.
• Not always intuitively understandable due to division by the mean of absolute values.
• Can give inflated errors for zero or near-zero values.

Due to these issues, alternatives are sometimes used, such as adjusted MAPE or other metrics that are more robust to zero values.