Part I Forecasting performance metrics

A$.$ MAPE $($and its complement $(1-$MAPE$)=$Forecast Accuracy$)$ are popular in business because of their alleged interpretability. Let$$s dig a little deeper.

Imagine you have a series of three actual sales and two forecasters:

Actual Sales Darnell$$s forecast Kade$$s forecast

$5010055$

$500050507000$

$10050110$

Darnell thinks his forecast is better, and Kade thinks their forecast is better. Who wins? You decide! $($You can just make sure all the following are in a table if that$$s easier$)$

$1.$ What is the MAPE for each forecaster? $(0\mathrm{.}2$ points$)$

$2.$ What is the forecast accuracy $(1-$MAPE$)$ for each forecaster? $(0\mathrm{.}2$ points$)$

$3.$ What is the MAE for each forecaster? $(0\mathrm{.}2$ points$)$

$4.$ What is the rMSE for each forecaster? $(0\mathrm{.}2$ points$)$

B$.$ Who is a $$better$$ forecaster? $($This may not be as simple as it sounds. If you did the above right, one forecast is better at one metric, and the other forecaster is better at the other metric. You task is to be able to articulate clearly why that is: what is each metric capturing that causes the switch?$)(0\mathrm{.}2$ points$)$ use $2-3$ sentences to explain your reasoning.

C$.$ Why is rMSE of Kade$$s forecast much bigger than that of Darnell$$s$?(0\mathrm{.}2$ points$)$ use $1$ sentence to explain your reasoning.