Question

In: Math

year Percentage 2000 28 2001 32 2002 37 2003 43 2004 47 2005 52 2006 56...

year Percentage
2000 28
2001 32
2002 37
2003 43
2004 47
2005 52
2006 56
2007 58
2008 61
2009 66
Forecast the percentage of tax returns that will be electronically filed for 2010 using exponential smoothing with trend adjustment. Set

alphaα =0.5 and β=0.6

Solutions

Expert Solution

Unadjusted forecast =(Percentage of prior period)+(1 - ​​​​) Forecast of the prior period.

(Unadjusted forecast of the first period is same as the actual).

Trend for the next period =(Forecast of that next period - Forecast of the prior period)+(1 - ​​​​​​)Trend of the prior period.

(Trend of the first period =0).

Adjusted forecast =Unadjusted forecast + Trend.

Year Percentage Unadjusted forecast ( =0.5) Trend ( =0.6) Adjusted forecast
2000 28 28 0 28
2001 32 0.5(28)+0.5(28) =28 0.6(28-28)+0.4(0) =0 28
2002 37 0.5(32)+0.5(28) =30 0.6(30-28)+0.4(0) =1.2 31.2
2003 43 0.5(37)+0.5(30) =33.5 0.6(33.5-30)+0.4(1.2) =2.58 36.08
2004 47 0.5(43)+0.5(33.5) =38.25 0.6(38.25-33.5)+0.4(2.58) =3.882 42.132
2005 52 0.5(47)+0.5(38.25) =42.625 0.6(42.625-38.25)+0.4(3.882) =4.1778 46.8028
2006 56 0.5(52)+0.5(42.625) =47.3125 0.6(47.3125-42.625)+0.4(4.1778) =4.48362 51.79612
2007 58 0.5(56)+0.5(47.3125) =51.65625 0.6(51.65625-47.3125)+0.4(4.48362) =4.399698 56.055948
2008 61 0.5(58)+0.5(51.65625) =54.828125 0.6(54.828125-51.65625)+0.4(4.399698) =3.6630042 58.4911292
2009 66 0.5(61)+0.5(54.828125) =57.9140625 0.6(57.9140625-54.828125)+0.4(3.6630042) =3.31676418 61.23082668
2010 0.5(66)+0.5(57.9140625) =61.95703125 0.6(61.95703125-57.9140625)+0.4(3.31676418) =3.752486922 65.70951817

Thus, the percentage of tax returns that will be electronically filed for 2010 using exponential smoothing with trend adjustment =65.70951817

milcah answered 1 year ago
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