Question

Consider the following annual series on the number of people assisted by a county’s human resources department.

Year: People:
1 22
2 24
3 28
4 24
5 22
6 24
7 20
8 26
9 24
10 28
11 26

a. What is the 3-year moving average for period 4?
b. What is the 3-year moving average forecast for period 12?
c. What is the Mean Square Error (MSE) for the 3-year moving average?
d. Using a smoothing constant of 0.4, what is the exponential smoothing value to be used as forecasts for period 4?
e. Using a smoothing constant of 0.4, what is the exponential smoothing value to be used as forecasts for period 12?
f. Using a smoothing constant of 0.4, what is the Mean Square Error (MSE) for exponential smoothing?

g. When comparing the accuracy of both forecasting techniques (3-year moving average and exponential smoothing with a 0.4 smoothing constant) we can conclude that

Answer 1

Answer on Question #57298-Math-Statistics and Probability

Consider the following annual series on the number of people assisted by a county's human resources department.

Year: People:

1 22

2 24

3 28

4 24

5 22

6 24

7 20

8 26

9 24

10 28

11 26

a. What is the 3-year moving average for period 4?

b. What is the 3-year moving average forecast for period 12?

c. What is the Mean Square Error (MSE) for the 3-year moving average?

d. Using a smoothing constant of 0.4, what is the exponential smoothing value to be used as forecasts for period 4?

e. Using a smoothing constant of 0.4, what is the exponential smoothing value to be used as forecasts for period 12?

f. Using a smoothing constant of 0.4, what is the Mean Square Error (MSE) for exponential smoothing?

g. When comparing the accuracy of both forecasting techniques (3-year moving average and exponential smoothing with a 0.4 smoothing constant) we can conclude that

Solution

a. The 3-year moving average for period 4 is

$$\frac{22 + 24 + 28}{3} = 24.67 \text{ rounded to } 25.$$

b. The 3-year moving average forecast for period 12 is

$$\frac{24 + 28 + 26}{3} = 26.$$

c. The Mean Square Error (MSE) for the 3-year moving average.

$$M S E = \frac {1 + 9 + 1 + 9 + 16 + 1 + 25 + 0}{8} = 7.75.$$

d.

The exponential smoothing value to be used as forecasts for period 4 is 25.

e. The exponential smoothing value to be used as forecasts for period 12 is 26.

f.

$$M S E = \frac {4 + 25 + 1 + 9 + 0 + 16 + 16 + 0 + 16 + 0}{10} = 8.7.$$

g. When comparing the accuracy of both forecasting techniques (3-year moving average and exponential smoothing with a 0.4 smoothing constant) we can conclude that 3-year moving average forecasting technique is more accurate in this example (7.75 < 8.7).

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