The MAPE could be employed in the context of regression problem and is defined by $$ MAPE := \frac{1}{n} \sum_{t=1}^{n} \left| \frac{y_{t} - \hat{y}_{t}}{y_{t}} \right| $$ where $y_{t}$ is target value and $\hat{y}_{t}$ is fitted value. In my intuition, it could be naturally generalized by $$ gMAPE := \frac{1}{n} \sum_{t=1}^{n} \frac{\left\| \mathbf{y}_{t} - \hat{\mathbf{y}}_{t} \right\|}{\left\| \mathbf{y}_{t} \right\|} $$ where $\left\| \cdot \right\|$ is any norm of a vector, but I have noticed there isn't reference or any mention about it. Is it weird or wrong? I think $gMAPE$ is more reasonalbe and useful in many case compare to univariate target(Empirically, '$\mathbf{y}_{t}$ must be not zero-vector' a is easier condition than '$y_{t}$ must be not zero' is '$\mathbf{y}_{t}$ must be not zero-vector'), why nobody is inter

The MAPE could be employed in the context of regression problem and is defined by $$ MAPE := \frac{1}{n} \sum_{t=1}^{n} \left| \frac{y_{t} - \hat{y}_{t}}{y_{t}} \right| $$ where $y_{t}$ is target value and $\hat{y}_{t}$ is fitted value. In my intuition, it could be naturally generalized by $$ gMAPE := \frac{1}{n} \sum_{t=1}^{n} \frac{\left\| \mathbf{y}_{t} - \hat{\mathbf{y}}_{t} \right\|}{\left\| \mathbf{y}_{t} \right\|} $$ where $\left\| \cdot \right\|$ is any norm of a vector, but I have noticed there isn't reference or any mention about it. Is it weird or wrong? I think $gMAPE$ is more reasonalbe and useful in many case compare to univariate target(Empirically, '$\mathbf{y}_{t}$ must be not zero-vector' a is easier condition than '$y_{t}$ must be not zero' is '$\mathbf{y}_{t}$ must be not zero-vector'), why nobody is interested it?