The sMAPE preference

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In the theory section, we mention how sMAPE is known to treat overestimation and underestimation unequally.

Let's consider the following scenario. We have true targets, YY, and for simplicity, Y={100}Y = \{100\}.

We have two models, M1M_1 and M2M_2, which produced the following predictions: Y1^={85}\hat{Y_1} = \{85\} and Y2^={115}\hat{Y_2} = \{ 115 \}.

Calculate their sMAPE and answer the following question: which model showed greater performance based on the sMAPE? Your answer function looks like this:

Answer={sMAPE1,if  M1showed better performancesMAPE2,otherwise\text{Answer}= \begin{cases} \text{sMAPE}_{1}, & \text{if }\ \text{M}_1\, \text{showed better performance} \\ \text{sMAPE}_2, & \text{otherwise} \end{cases}

Round the answer up to the third decimal. Use the modified sMAPE formula (the one that outputs in the 0100%0-100\% range).

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