# Forecasting

**Topics:**1977, 1981, 2006

**Pages:**5 (623 words)

**Published:**July 1, 2014

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 on the same graph. b. Compute the seasonal indexes for the four quarters.

c. When does Hudson Marine experience the largest seasonal effect? Does this result seem reasonable? Explain.

Q3

Eddie’s Restaurants collected the following relationship between advertising and sales sample of five restaurants;

Advertising Expenditures

($1000s)

1

4

6

10

14

Sales

(1000s)

19

44

40

52

53

a. Let x represent advertising expenditures and y represent sales. Use the method of least squares to develop a straight-line approximation of the relationship between the two variables.

b. Use the equation developed in part (a) to forecast sales for an advertising expenditure of $8,000.

c. Determine the correlation coefficient between the two variables (advertising expenditures and sales). What is your observation?

A1

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

Dec 15

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

Simple moving average

Fund

Month

Price

22-Sep 37.8750

29-Sep 35.6250

6-Oct 34.6875

13-Oct 33.5625

20-Oct 32.6250

27-Oct 34.0000

3-Nov 33.6250

10-Nov 35.0625

17-Nov 34.0625

24-Nov 34.1250

1-Dec 33.2500

8-Dec 32.0625

15-Dec

Weighted moving average

Forecast

error

Forecast

error

Squared

error

Squared

error

Exponential smoothing

Forecast

error

Squared

error

37.8750

-2.2500

5.0625

37.0875

-2.4000

5.7600

α = 0.35

37.8750

36.0625

-2.5000

6.2500

35.7000

-2.1375

4.5689

36.2475

-2.6850

7.2092

34.6250

-2.0000

4.0000

34.4250

-1.8000

3.2400

35.3078

-2.6828

7.1971

33.6250

0.3750

0.1406

33.4125

0.5875

0.3452

34.3688

-0.3688

0.1360

33.3958

0.2292

0.0525

33.3625

0.2625

0.0689

34.2397

-0.6147

0.3779

33.4167

1.6458

2.7088

33.5750

1.4875

2.2127

34.0246

1.0379...

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