Period Actual

Forecast Error $(|$A$-$F$|)$

MA$5$ WMA$(0\mathrm{.}5,0\mathrm{.}3,0\mathrm{.}2)$ ES$(\backslash$alpha $=0\mathrm{.}2)$ E$-$MA$5$ E$-$WMA E$-$ES$(0\mathrm{.}2)$

$2006$ January $1779$

February $2802$

March $3818$

April $4888$

May $5898$

June $6902$

July $7916$

August $8708$

September $9695$

October $10708$

November $11716$

December $12784$

$2007$ January $13845$

February $14739$

March $15871$

April $16927$

May $171133$

June $181124$

July $191056$

August $20889$

September $21857$

October $22772$

November $23751$

December $24820$

$2008$ January $25857$

February $26881$

March $27937$

April $281159$

May $291072$

June $301246$

July $311198$

August $32922$

September $33798$

October $34879$

November $35945$

December $36990$

$2009$ January $37917$

February $38956$

March $391001$

April $401142$

May $411276$

June $421356$

July $431288$

August $441082$

September $45877$

October $461009$

November $471100$

December $48998$

$2010$ January $49887$

February $50892$

March $51997$

April $521118$

May $531197$

June $541256$

July $551202$

August $561170$

September $57982$

October $581297$

November $591163$

December $601053$

Using the $60-$period data shown in Exhibit $1(2006$ January as period $1$; $2006$ December as period $12$; $2007$ January as period $13$; $2010$ December as period $60,$ and so on$),$ we are interested in forecasting the transformer requirement in the future. We would like to select the best method from $(1)$ a $5-$period moving average, $(2)$ a weighted moving average with weights $(0\mathrm{.}5,0\mathrm{.}3,0\mathrm{.}2),$ and $(3)$ an exponential smoothing method with a smoothing constant of $0\mathrm{.}2.$ To this end, we need to compute the MAD for each method. Hint, when calculating MAD, you need to forecast and calculate forecasting errors for all possible periods $($whenever applicable$).$ For example, when working on MAD for a $5-$period moving average, you need to forecast from period $6$ to period $60.$