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The U$.$S$.$ monthly inflation rate for $2020$ is shown below:

$\backslash$table$[[$MONTH$,$INFLATION $(\%),$MONTH,INFLATION $(\%)],[$January$,2\mathrm{.}5,$July,$1\mathrm{.}0],[$February$,2\mathrm{.}3,$August,$1\mathrm{.}3],[$March$,1\mathrm{.}5,$September,$1\mathrm{.}4],[$April$,0\mathrm{.}3,$October,$1\mathrm{.}2],[$May$,0\mathrm{.}1,$November,$1\mathrm{.}2],[$June$,0\mathrm{.}7,$December,$1\mathrm{.}4]]$

a$.$ Compute the inflation rate for January $2021$ using the exponential smoothing forecast using $=0\mathrm{.}4$ and then using $0\mathrm{.}6.$ Assume that the forecast for January $2020$ is $2\mathrm{.}5.$ Do not round intermediate calculations. Round your answers to three decimal places.

Forecast $($January $2021,a=0\mathrm{.}4)$:

$\%$

Forecast $($January $2021,a=0\mathrm{.}6)$: $\%$

b$.$ What is the MAD for the forecasts generated using exponential smoothing method? Use only the months from March to December. Do not round intermediate calculations, Round your answers to three decimal places.

$)=(0\mathrm{.}4$ : p$.$p$.$

$)=(0\mathrm{.}6$ p$.$p$.$

Which method is better?

The exponential smoothing with a smoothing constant of is better because it provides a MAD.