# Forecasting

Topics: 1977, 1981, 2006 Pages: 5 (623 words) Published: July 1, 2014
FORECASTING
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

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

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;
(\$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...