Root Relative Squared Error (RSE)

The Root Relative Squared Error (RSE) is an evaluation metric in time series forecasting,1

$$ \mathrm{RSE} = \frac{ \sqrt{ \sum_{i, t} ( y^{(i)}_t - \hat y^{(i)}_t )^2 } }{ \sqrt{ \sum_{i, t} ( y^{(i)}_t - \bar y )^2 } } $$

where $y^{(i)}$ is the $i$th time series, ${} _ t$ denotes the time step $t$, and $\bar y$ is the mean of the forecasted series, i.e., $\bar y = \operatorname{mean}(y^{(i\in\{0, 1, \cdots, N\})} _ { t\in \{T _ f, T _ {f+1}, \cdots T _ {f+H}\} })$.


  1. Lai2017 Lai G, Chang W-C, Yang Y, Liu H. Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks. arXiv [cs.LG]. 2017. Available: http://arxiv.org/abs/1703.07015  ↩︎

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Lei Ma (2022). 'Root Relative Squared Error (RSE)', Datumorphism, 08 April. Available at: https://datumorphism.leima.is/cards/time-series/ts-rse/.