Before you begin Exercise $1,$ let$$s check that you have the right data! The average should be $1617!$

Once you identify and develop an appropriate exponential smoothing model with the starting values for parameter$($s$)=0\mathrm{.}5,$ what are the following numerical values:

$1.$ The within$-$sample forecast for January $2023.$

$2.$ The out$-$of$-$sample forecast for October $2023.$

$3.$ The out$-$of$-$sample forecast for June $2024.$

$4.$ The MAPE.

$5.$ The MAE.

Critically think for a way to optimise alpha and beta $($if there is no beta, you can input $0$ for question $7)$ via the MSE, and report the following values after your optimisation:

$6.$ Alpha.

$7.$ Beta.

$8.$ The MAPE.

$9.$ The within$-$sample forecast for January $2023.$

$10.$ The out$-$of$-$sample forecast for June $2024.$