Q1:

Moving averages are often used to identify movements of stock prices. Weekly closing prices (in $ per share) for Toys Я Us for 22 September, 1997, through December 8, 1997, are as follows (Prudential Securities Inc);

Month

Sept 22

Sept 29

Oct 6

Oct 13

Oct 20

Oct 27

Nov 3

Nov 10

Nov 17

Nov 24

Dec 1

Dec 8

Fund Price

37.8750

35.6250

34.6875

33.5625

32.6250

34.0000

33.6250

35.0625

34.0625

34.1250

33.2500

32.0625

a. Use a 3-month simple moving average to smooth the time series. Forecast the closing price for December 15, 1997.

b. Use a 3-month weighted moving average to smooth the time series. Use a weight of 0.4 for the most recent period, 0.4 for the next period back, and 0.2 for the third period back. Forecast the closing price for December 15, 1997.

c. Use exponential smoothing with a smoothing constant of α = 0.35 to smooth the time series. Forecast the closing price for December 15, 1997.

d. Which of the three methods do you prefer? Why?

Q2:

Hudson Marine has been an authorized dealer for C&D marine radios for the past 7 years.

The number of radios sold each year is shown below:

Year

1

2

3

4

5

6

7

Number of radios sold

35

50

75

90

105

110

130

a. Graph this time series. Does a linear trend appear?

b. Develop the equation for the linear trend component for the time series.

c. Use the linear trend developed in part (b) to prepare a forecast sale in year 8.

d. Use the linear trend developed in part (b), make a forecast for year 10.

Suppose that the following are the quarterly sales data for the past 7 years.

Year

1

2

3

4

5

6

7

Quarter

1

6

10

14

19

22

24

28

Quarter

2

15

18

26

28

34

36

40

Quarter

3

10

15

23

25

28

30

35

Quarter

4

4

7

12

18

21

20

27

Number of radios sold 35

50

75

90

105

110

130

a. Show the 4-quarter moving average values for this time series. Plot both the original time series and the moving averages