📂Data Science

Mean Arctangent Absolute Percentage Error MAAPE

Definition ¹

In a regression problem, for a data point $\left\{ x_{k} \right\}_{k=1}^{n}$ and its prediction $\left\{ \widehat{x}_{k} \right\}_{k=1}^{n}$, the Mean Arctangent Absolute Percentage Error is defined as follows: $$\text{MAAPE} = {{ 1 } \over { n }} \sum_{k=1}^{n} \arctan \left| {{ x_{k} - \widehat{x}_{k} } \over { x_{k} }} \right|$$

Explanation

MAAPE is a metric that resolves the critical flaw of MAPE, which may diverge to infinity and is not actually bounded, simply by taking the arctangent. This idea was presented by Korean authors Sung-Il Kim and Hee-Kyung Kim in their 2016 paper in the International Journal of Forecasting, and as of 2024, it boasts over 1000 citations. The authors modified the formula so that metrics like MAPE can also be applied to intermittent time series data, as suggested in the title of their paper. According to this, it can be inferred that its utility is not lost even in all data with sparse characteristics, not just in time series.

Under an accurate prediction as shown in $x_{k} = \widehat{x}_{k}$, AAPE is $0$. When $x_{k} \ne \widehat{x}_{k}$, AAPE for a data point with $x_{k} = 0$ is $\pi / 2$. Contrary to MAPE, the closer to $0$, the better the performance, and $\pi / 2$ is the worst value.

See Also

• Mean Absolute Percentage Error