Empirical Correlation Coefficient (CORR)

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#Time Series #Forecasting

The Empirical Correlation Coefficient (CORR) is an evaluation metric in time series forecasting,1

$$ \mathrm{CORR} = \frac{1}{N} \sum_{i=1}^N \frac{ \sum_t (y^{(i)}_t - \bar y^{(i)} ) ( \hat y^{(i)}_t -\bar{ \hat y}^{(i)} ) }{ \sqrt{ \sum_t (y^{(i)}_t - \bar y^{(i)} )^2 ( \hat y^{(i)}_t -\bar{\hat y}^{(i)} )^2 } } $$

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

  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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References:
  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). 'Empirical Correlation Coefficient (CORR)', Datumorphism, 08 April. Available at: https://datumorphism.leima.is/cards/time-series/ts-corr/.