6
$\begingroup$

Göçken et al. define the root mean square percentage error (RMSPE) as \begin{equation} \text{RMSPE} = \sqrt{\frac{100\%}{n} \cdot \sum_{i=1}^n \Delta X^2_{\text{rel},i}} \end{equation} with \begin{equation} \Delta X_{\text{rel},i}=\frac{X_i}{T_i}-1, \end{equation} where $T_i$ is the desired value and $X_i$ is the actual value.

However, Göçken et al. and Webber et al. define the root mean square relative error (RMSRE) as:

\begin{equation} \text{RMSRE} = \sqrt{\frac{1}{n}\cdot\sum_{i=1}^{n}\Delta X^2_{\text{rel},i}} \end{equation}

If we express the actual error $\Delta X_{\text{rel},i}$ as a percentage and name it $\Delta X_{\%,i}$, then we have: \begin{equation} \Delta X_{\%,i}=\left(\frac{X_i}{T_i}-1\right)\cdot 100\%=\Delta X_{\text{rel},i} \cdot 100\% \end{equation}

From my understanding, RMSPE should be the same as RMSRE, where $\Delta X_{\text{rel},i}$ is substituted by $\Delta X_{\text{%},i}$. However, this would yield \begin{equation} \text{RMSPE} = \sqrt{\frac{1}{n} \cdot \sum_{i=1}^n \Delta X^2_{\text{rel},i}} \cdot 100\%, \end{equation} which differs from the original definition of Göçken et al. by a factor of 10. Are my considerations correct and if so, are there alternative sources for the RMSPE?

$\endgroup$
2
  • $\begingroup$ $\sqrt{100\%}=100\%=1$. There is no factor of $10$ difference, though putting it inside the square root is misleading. $\endgroup$
    – robjohn
    Jun 8, 2022 at 8:24
  • $\begingroup$ That... makes sense. And it just took 3 years for someone to point it out. :-) Thanks a lot! $\endgroup$
    – Nos
    Jun 8, 2022 at 8:55

1 Answer 1

7
$\begingroup$

There are several alternative sources (Swanson et al., Fomby, Shcherbakov et al.), which agree that the RMSPE is defined as: \begin{equation} \text{RMSPE} = \sqrt{\frac{1}{n} \cdot \sum_{i=1}^n \Delta X^2_{\text{rel},i}} \cdot 100\% \end{equation}

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.