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=0.9=0.9and w=0.3=0.3). (Note: The exponential smoothing forecasts may be begun by assuming Yt+1=Yt^t+1=.)

Year	Actual Demand	Moving Average	Exponential Smoothing
(5-year)	(3-year)	(W = 0.9)	(W = 0.3)
2000	1,100
2001	1,105
2002	1,125
2003	1,160
2004	1,210
2005	1,195
2006	1,195
2007	1,210
2008	1,240
2009	1,285
2010	*

The following table shows the square errors, (YtYt-1)2^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	3,025	900	100	2,025
2006	1,296	49	1	961
2007	1,089	100	225	1,369
2008	2,116	1,600	961	3,136
2009	5,625	4,900	2,304	7,056
RMSE

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

Five-year moving average

Exponential smoothing (w = 0.3)

Exponential smoothing (w = 0.9)

Three-year moving average