Chapter 6 – Time Series Analysis & Forecasting
50. The number of properties newly listed with a real estate agency in each quarter over the last four years is given below.
Assume the time series has seasonality without trend.
Year
Quarter 1 2 3 4
1 73 81 76 77
2 89 87 91 88
3 123 115 108 120
4 92 95 87 97
a. Develop the optimization model that finds the estimated regression equation that minimize the sum of squared error.
b. Solve for the estimated regression equation.
c. Forecast the four quarters of Year 5.
51. Quarterly billing for water usage is shown below.
Year
Quarter 1 2 3 4
Winter 64 66 68 73
Spring 103 103 104 120
Summer 152 160 162 176
Fall 73 72 78 88
a. Solve for the forecast equation that minimizes the sum of squared error.
b. Forecast the summer of year 5 and spring of year 6.
Chapter 6 – Time Series Analysis & Forecasting
52. A customer comment phone line is staffed from 8:00 a.m. to 4:30 p.m. five days a week. Records are available that
show the number of calls received every day for the last five weeks.
Week Day Number Week Day Number
1 M 28 4 M 27
T 12 T 13
W 16 W 16
TH 15 TH 18
F 23 F 24
2 M 25 5 M 26
T 10 T 11
W 14 W 18
TH 14 TH 17
F 26 F 25
3 M 32
T 15
W 15
TH 13
F 21
a. Develop the optimization model that finds the estimated regression equation that minimize the sum of squared error.
b. Solve for the estimated regression equation.
c. Forecast the five days of week 6.
53. Monthly sales at a coffee shop have been analyzed. The seasonal index values are
Month Index
Jan 1.38
Chapter 6 – Time Series Analysis & Forecasting
Feb 1.42
Mar 1.35
Apr 1.03
May .99
June .62
July .51
Aug .58
Sept .82
Oct .82
Nov .92
Dec 1.56
and the trend line is 74123 + 26.9(t). Assume there is no cyclical component and forecast sales for year 8 (months 97 –
54. A 24-hour coffee/donut shop makes donuts every eight hours. The manager must forecast donut demand so that the
bakers have the fresh ingredients they need. Listed below is the actual number of glazed donuts (in dozens) sold in each of
the preceding 13 eight-hour shifts.
Date Shift Demand(dozens)
June 3 Day 59
Evening 47
Night 40
June 4 Day 64
Evening 43
Night 39
June 5 Day 62
Evening 46
Night 42
June 6 Day 60
Evening 45
Night 40
June 7 Day 58
a. Develop the optimization model that finds the estimated regression equation that minimize the sum of squared error.
b. Solve for the estimated regression equation.
c. Forecast the demand for glazed donuts for the Day, Evening, and Night shifts of June 8.
Chapter 6 – Time Series Analysis & Forecasting
55. The number of plumbing repair jobs performed by Auger’s Plumbing Service in each of the last nine months are listed
below.
Month Jobs Month Jobs Month Jobs
March 353 June 374 September 399
April 387 July 396 October 412
May 342 August 409 November 408
a. Assuming a linear trend function, forecast the number of repair jobs Auger’s will perform in December using the
least squares method.
b. What is your forecast for December using a three-period weighted moving average with weights of .6, .3, and .1?
How does it compare with your forecast from part (a)?
56. Quarterly revenues (in $1,000,000’s) for a national restaurant chain for a five-year period were as follows:
Quarter Year 1 Year 2 Year 3 Year 4 Year 5
1 33 42 54 70 85
2 36 40 53 67 82
3 35 42 54 70 87
4 38 47 62 77 99
a. Solve for the forecast equation that minimizes the sum of squared error.
b. Forecast the four quarters of year 6.
Chapter 6 – Time Series Analysis & Forecasting
57. Business at Terry’s Tie Shop can be viewed as falling into three distinct seasons: (1) Christmas (November-
December); (2) Father’s Day (late May – mid-June); and (3) all other times. Average weekly sales (in $’s) during each of
these three seasons during the past four years has been as follows:
Season Year 1 Year 2 Year 3 Year 4
1 1856 1995 2241 2280
2 2012 2168 2306 2408
3 985 1072 1105 1120
Determine a forecast for the average weekly sales in years 5 and 6 for each of the three seasons.
58. Sales (in thousands) of the new Thorton Model 506 convection oven over the eight-week period since its introduction
have been as follows:
Week Sales
1 18.6
2 21.4
3 25.2
4 22.4
5 24.6
6 19.2
7 21.7
8 23.8
a. Which exponential smoothing model provides better forecasts, one using α = .6 or α = .2? Compare them using mean
squared error.
b. Using the two forecast models in part (a), what are the forecasts for week 9?
59. Coyote Cable has been experiencing an increase in cable service subscribers over the last few years due to increased
advertising and an influx of new residents to the region. The numbers of subscribers (in 1000’s) for the last 16 months are
as follows:
Month Sales Month Sales Month Sales
1 12.8 7 20.6 12 23.8
2 14.6 8 18.5 13 25.1
Chapter 6 – Time Series Analysis & Forecasting
3 15.2 9 19.9 14 24.7
4 16.1 10 23.6 15 26.5
5 15.8 11 24.2 16 28.9
6 17.2
Forecast the number of subscribers for months 17, 18, 19, and 20.
60. Weekly sales of the Weber food processor for the past ten weeks have been:
Week Sales Week Sales
1 980 6 990
2 1040 7 1030
3 1120 8 1260
4 1050 9 1240
5 960 10 1100
a. Determine, on the basis of minimizing the mean square error, whether a three-period or four-period simple moving
average model gives a better forecast for this problem.
b. For each model, forecast sales for week 11.
61. Below you are given information on John’s Hair Salon profit for the past 7 years.
Year Profit (In Thousands)
1 15.0
2 16.2
3 17.1
4 18.1
5 18.8
6 19.2
7 20.5
a. Use regression analysis to obtain an expression for the linear trend projection.
b. Forecast John’s Hair Salon profit for the next 5 years.
Chapter 6 – Time Series Analysis & Forecasting
62. Community General Hospital finds itself treating many bicycle accident victims. Data from the last seven 24-hour
periods is shown below:
Day Bicycle Victims
1 6
2 8
3 4
4 7
5 9
6 9
7 7
a. What are the forecasts for days 4 through 8 using a 3-period moving average model? Round the forecasts to two
decimal places.
b. With an alpha value of .4 and a starting forecast in day 3 equal to the actual data, what are the exponentially smoothed
forecasts for days 4 through 8? Round the forecasts to two decimal places.
c. What is the MAD for the 3-period moving average forecasts for days 4 through 7? Compare it to the MAD for the
exponential smoothing forecasts for days 4 through 7.
63. State Division of Motor Vehicles (DMV) statistics show the rate of new driver’s license applications to be as shown
below:
Month Week Applications
April 1 238
2 199
3 215
4 212
May 1 207
2 211
3 196
4 206
a. Using a 3-week moving average, what is the forecast for the first week in June?
Chapter 6 – Time Series Analysis & Forecasting
b. Using a 5-week moving average, what is the forecast for the first week in June?
c. Using weights of .4 (newest), .3, .2, and .1 (oldest), what is the 4-week weighted moving average forecast for the first
week in June?
d. Using weights of .6 (newest), .3, and .1 (oldest), what is the 3-week weighted moving average forecast for the first
week in June?
64. Consider the sales for six consecutive weeks for Sam’s Strawberries. The sales are in “flats” sold.
Week Sales
1 16
2 18
3 14
4 10
5 20
6 22
a. Using a moving average with AP = 3, forecast the sales for weeks four through six.
b. Use a weighted moving average with weights of .5 (most recent), .4, and .1 (oldest) to predict the sales for weeks four
through six.
c. Use the naïve approach to predict the sales for weeks four through six.
d. Use exponential smoothing with = .3 to forecast sales for weeks four through six.
e. Use MAD to pick the best of the four forecasting methods used in a) through d).
Chapter 6 – Time Series Analysis & Forecasting
65. Consider the sales for six consecutive weeks for Sam’s Strawberries. The sales are in “flats” sold.
Week Sales
1 16
2 18
3 14
4 10
5 20
6 22
Use linear regression (time series) to develop a prediction equation that will forecast sales. Then use that prediction
equation to get the forecast for week seven.
66. A Taiwan electronics company exports personal computers (PCs) to the U.S. Their PC sales (in thousands) over the
past five months are given below:
Month Sales
1 6
2 9
3 13
4 15
5 20
Chapter 6 – Time Series Analysis & Forecasting
a. What is the regression equation if the company wants to predict sales?
b. What is the forecast for sales in month 6?
Essay
67. Explain what conditions make quantitative forecasting methods appropriate.
68. What is a stable time series, and what forecasting methods are appropriate for one?
69. How can error measures be used to determine the number of periods to use in a moving average? What are you
assuming about the future when you make this choice?
70. Discuss the effects of using a small smoothing constant value and when it is most appropriate to use. Then, do the
same for a large smoothing constant value.
71. Explain and contrast three measures of forecast accuracy.
Chapter 6 – Time Series Analysis & Forecasting
72. Describe a time series plot and discuss its purpose and when in the forecasting process it should be constructed.