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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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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

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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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