sMAPE
Definition
The correctness metric for the Chaotic Function Prediction task.
Symmetric mean absolute percentage error (sMAPE), a standard metric in forecasting, is used to measure the correctness of the model predictions \(\hat{y_i}\) against the ground-truth \(y_i\), over \(n\) data points in the test split of the time series. The sMAPE metric has a bounded range of \([0, 200]\), thus diverging predictions (infinity or NaN) due to floating-point arithmetic have bounded error which can be used to average correctness over multiple time series instantiations.
\[sMAPE = 200 \times \frac{1}{n} \left( \sum_{i=1}^{n} \frac{|y_i - \hat{y_i}|}{(|y_i| + |\hat{y_i}|)}\right)\]