Forecasting

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

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