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., $\bar y = \operatorname{mean}(y^{(i\in\{0, 1, \cdots, N\})} _ { t\in \{T _ f, T _ {f+1}, \cdots T _ {f+H}\} })$.

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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/.