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)