ASSIGNMENT 1: FORECASTING BOX OFFICE RETURNS
For years, people in the motion picture industry—critics, film historians, and others—have eagerly awaited the second
issue in January of Variety. Long considered the show business bible, Variety is a weekly trade newspaper that reports
on all aspects of the entertainment industry: movies, television, recordings, concert tours, and so on. The second issue
in January, called the Anniversary Edition, summarizes how the entertainment industry fared in the previous year, both
artistically and commercially.
In this issue, Variety publishes its list of All Time Film Rental Champs. This list indicates, in descending order,
motion pictures and the amount of money they returned to the studio. Because a movie theater rents a film from a
studio for a limited time, the money paid for admission by ticket buyers is split between the studio and the theater
owner. For example, if a ticket buyer pays $8 to see a particular movie, the theater owner keeps about $4 and the studio
receives the other $4. The longer a movie plays in a theater, the greater the percentage of the admission price returned
to the studio. A film playing for an entire summer could eventually return as much as 90% of the $8 to the studio. The
theater owner also benefits from such a success because although the owner's percentage of the admission price is
small, the sales of concessions (candy, soda, and so on) provide greater profits. Thus, both the studio and the theater
owner win when a film continues to draw audiences for a long time. Variety lists the rental figures (the actual dollar
amounts returned to the studios) that the films have accrued in their domestic releases (United States and Canada).
In addition, Variety provides a monthly Box-Office Barometer of the film industry, which is a profile of the
month's domestic box office returns. This profile is not measured in dollars, but scaled according to some standard. By
the late 1990s, for example, the scale was based on numbers around 100, with 100 representing the average box office
return of 1995. The figures from 2001 through 2010 are given in the table.
All the figures are scaled around 2000s box office returns, but instead of dollars, artificial numbers are used. Film
executives can get a relative indication of box office figures compared to the arbitrary 1995 scale. For example, in
January 2001, the box office returns to the film industry were 95% of the average that year, whereas in January 2002,
the returns were 104% of the average of 1995 (or, they were 4% above the average of 1990s figure).
Month
2001
2002
2003
January
95
104
10A
February
March
April
94
98
96
95
115
107
104
9A
11B
9C
10D
10B
9C
8D
89
108
109
101
10A
10B
7C
11D
9B
8C
8D
85
124
134
109
12A
11B
10C
11D
May
June
July
August
September
October
November
December
2004
2005
2006
2007
2008
2009
2010
8A
132
11B
12C
11D
114
169
131
139
12A
11B
11C
12D
109
101
111
140
179
145
140
120
129
118
139
125
111
12A
11A
14A
118
121
140
141
201
152
138
137
138
144
148
123
121
139
119
156
154
136
105
132
123
164
12B
13C
10D
115
149
155
129
11A
16B
15C
17D
14B
16C
13D
124
168
159
137
14A
15B
17C
19D
14B
13C
14D
141
191
178
156
11A
13B
17C
18D
From the time series given in the table, you will make a forecast for the 12 months of the next year, 2011.
1. Produce a line graph of the data over time. From this graph, do you see a pattern? Can you detect any seasonality
in the data?
2. Use Stationary Data With Additive Seasonal Effects. Comment on the appropriateness of this method on data set.
Use Solver to find the optimal (minimal MSE) alpha and beta. Plot the predictions from this model on the graph
with the original data. How well does this technique fit the data? Make forecasts for the 12 months of 2011.
3. Use regression to build a quadratic trend model. Comment on the goodness-of-fit of this model to the data. Plot the
predictions from this model on the graph with the original data. How well does this technique fit the data?
4. Use Holt-Winter's additive method. Comment on the appropriateness of Holt-Winter's additive method on this data
set. Use Solver to find the optimal (minimal MSE) constants. Plot the predictions from this model on the graph with
the original data. How well does this technique fit the data? What are your forecasts for the 12 months of 2011?
5. Develop multiplicative seasonal indices for the linear trend model developed in question 4. Use these indices to
adjust predictions from the linear trend model for seasonal effects. Plot the predictions from this model on the
graph with the original data. How well does this technique fit the data? Make forecasts for the 12 months of 2011
using this technique.
6. Using mean squared error as your criterion; in which forecasting method of those you tried do you have the most
confidence for making accurate forecasts for 2011?