Question $15(5$ points$)$

Ten months of data and the forecasts for those same periods are in the table below. Create an exponential smoothing forecast for February onwards, assuming that the January forecast was $42.$ Which value of alpha gives the best forecast using the MAPE criterion?

Month Actual

January $42$

February $58$

March $58$

April $,77$

May : $91$

June $,102$

JUI $,124$

August $148$

Septenber $171$

Sttober $177$

ipha $=0\mathrm{.}4$

atplite $=0\mathrm{.}3$

$3p{n}_1=0\mathrm{.}2$