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=0.9and 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	1,300
2001	1,325
2002	1,375
2003	1,370
2004	1,390
2005	1,435
2006	1,425
2007	1,440
2008	1,480
2009	1,465
2010	*

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	6,889	3,249	2,209	6,241
2006	2,116	729	25	2,025
2007	1,681	576	196	2,116
2008	4,624	2,209	1,681	5,184
2009	961	289	121	1,225
RMSE

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

Exponential smoothing (w = 0.9)

Exponential smoothing (w = 0.3)

Three-year moving average

Five-year moving average