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 Yˆt + 1=YtY^t + 1=Yt.) Year Actual Demand Moving Average Exponential Smoothing (5-year) (3-year) (W = 0.9) (W = 0.3) 2000 800 2001 790 2002 785 2003 785 792 2004 790 787 2005 805 790 787 2006 825 791 794 2007 850 798 807 2008 825 811 827 2009 860 819 834 2010 * 833 846 The following table shows the square errors, (Yt−Yˆt - 1)2Yt−Y^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 225 324 225 196 2006 1,156 961 441 900 2007 2,704 1,849 729 2,116 2008 196 4 484 49 2009 1,681 676 1,089 1,600 RMSE Based on the RMSE criterion, which of the forecasting methods is the most accurate? Exponential smoothing (w = 0.9) Five-year moving average Exponential smoothing (w = 0.3) Three-year moving average

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...

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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 Yˆt + 1=YtY^t + 1=Yt.)

Year	Actual Demand	Moving Average	Exponential Smoothing
(5-year)	(3-year)	(W = 0.9)	(W = 0.3)
2000	800
2001	790
2002	785
2003	785		792
2004	790		787
2005	805	790	787
2006	825	791	794
2007	850	798	807
2008	825	811	827
2009	860	819	834
2010	*	833	846

The following table shows the square errors, (Yt−Yˆt - 1)2Yt−Y^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	225	324	225	196
2006	1,156	961	441	900
2007	2,704	1,849	729	2,116
2008	196	4	484	49
2009	1,681	676	1,089	1,600
RMSE