Forecast Errors: MAPE, sMAPE and MASE

Implement three forecast accuracy metrics (as percentages for the first two):

• mape(y, f) = $\frac{100}{n}\sum\left|\frac{y - f}{y}\right|$, skipping points where $y = 0$
• smape(y, f) = $\frac{100}{n}\sum\frac{|y - f|}{(|y| + |f|)/2}$, counting a term as 0 when both are 0
• mase(y, f, y_train, m=1) = MAE of the forecast divided by the in-sample MAE of the seasonal naive forecast on y_train (lag m)