a$)$ Use a $3-$month moving average on all the data and plot the averages and the prices.

b$)$ Use a $3-$month weighted moving average and add the $3-$month weighted plot to the graph created in part $($a$).$ Weights are as list: $0\mathrm{.}1,0\mathrm{.}3,0\mathrm{.}6,$ where the heavier weight be applied to the more recent month.

c$)$ Which is better $($using MAPE$)$: the $3-$month average or the $3-$month weighted average?

d$)$ Compute the forecasts for each month using exponential smoothing, with an initial forecast for January of $$1\mathrm{.}80.$ Use $\backslash$alpha $=\mathrm{.}1$ and $\backslash$alpha $=\mathrm{.}5.$ Using MSE, which a is the best?

Please attach your paperwork or Excel spreadsheet to show the solving steps.