Question: 5. Exercise 5.5 A firm experienced the demand shown in the following table. Fill in the table by preparing forecasts based on a five-year moving

5. Exercise 5.5

A firm experienced the demand shown in the following table.

Fill in the table by preparing forecasts based on a five-year moving average, a three-year moving average, and exponential smoothing (w=0.9w=0.9 and w=0.3w=0.3 ). (Note: The exponential smoothing forecasts may be begun by assuming Yt + 1=YtY^t + 1=Yt .)

Year

Actual Demand

Moving Average

Exponential Smoothing

(5-year)

(3-year)

(W = 0.9)

(W = 0.3)
2000 1,500
2001 1,545 selector 1
  • 1,500
  • 1,774
  • 1,608
 selector 2
  • 1,615
  • 1,627
  • 1,500
2002 1,585 selector 3
  • 1,693
  • 1,314
  • 1,541
 selector 4
  • 1,541
  • 1,514
  • 1,314
2003 1,620 selector 5
  • 1,774
  • 1,543
  • 1,608
 selector 6
  • 1,774
  • 1,581
  • 1,994
 selector 7
  • 1,581
  • 1,535
  • 1,774
2004 1,650 selector 8
  • 1,314
  • 1,583
  • 1,653
 selector 9
  • 1,314
  • 1,616
  • 1,489
 selector 10
  • 1,616
  • 1,561
  • 1,314
2005 1,675 selector 11
  • 1,627
  • 1,580
  • 1,615
 selector 12
  • 1,650
  • 1,693
  • 1,618
 selector 13
  • 1,650
  • 1,647
  • 1,627
 selector 14
  • 1,588
  • 1,627
  • 1,647
2006 1,695 selector 15
  • 1,970
  • 1,615
  • 1,655
 selector 16
  • 1,648
  • 1,994
  • 1,653
 selector 17
  • 1,994
  • 1,672
  • 1,970
 selector 18
  • 1,970
  • 1,672
  • 1,614
2007 1,710 selector 19
  • 1,454
  • 1,660
  • 1,645
 selector 20
  • 1,489
  • 1,673
  • 1,683
 selector 21
  • 1,454
  • 1,693
  • 1,489
 selector 22
  • 1,638
  • 1,693
  • 1,454
2008 1,720 selector 23
  • 1,695
  • 1,670
  • 1,793
 selector 24
  • 1,828
  • 1,693
  • 1,708
 selector 25
  • 1,793
  • 1,708
  • 1,828
 selector 26
  • 1,708
  • 1,793
  • 1,660
2009 1,725 selector 27
  • 1,690
  • 1,286
  • 1,725
 selector 28
  • 1,298
  • 1,728
  • 1,708
 selector 29
  • 1,719
  • 1,286
  • 1,298
 selector 30
  • 1,719
  • 1,678
  • 1,286
2010 * selector 31
  • 1,765
  • 1,637
  • 1,705
 selector 32
  • 1,632
  • 1,718
  • 1,743
 selector 33
  • 1,724
  • 1,637
  • 1,632
 selector 34
  • 1,724
  • 1,637
  • 1,692

The following table shows the square errors, (YtYt - 1)2YtY^t - 12 , for forecasts from 2005 through 2009.

Fill the table by calculating the root mean square error (RMSE) for each of the methods.

Year

Square Error

Moving Average

Exponential Smoothing

(5-year)

(3-year)

(W = 0.9)

(W = 0.3)
2005 9,025 3,249 784 7,569
2006 6,400 2,209 529 6,561
2007 4,225 1,369 289 5,184
2008 2,500 729 144 3,600
2009 1,225 289 36 2,209
RMSE selector 1
  • 68.37
  • 39.61
  • 70.88
  • 18.88
 selector 2
  • 68.37
  • 39.61
  • 18.88
  • 70.88
 selector 3
  • 68.37
  • 18.88
  • 39.61
  • 70.88
 selector 4
  • 18.88
  • 70.88
  • 39.61
  • 68.37

Points:

Based on the RMSE criterion, which of the forecasting methods is the most accurate?

Five-year moving average

Exponential smoothing (w = 0.3)

Three-year moving average

Exponential smoothing (w = 0.9)

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