Case Study - Complete case study on forecasting:
Case Study : Forecasting Box Office Returns
Managerial Report is needed
Produce a time series plot of the data. From this graph, do you see a pattern? Can you see any seasonality in the data?
Use exponential smoothing to fit the data. Select an appropriate constant α based on the variation you see in the data. Comment on the appropriateness of exponential smoothing on this data set. Plot the predictions from this model on the graph with the original data. How well does this technique fit the data? Make forecasts for 1997.
Use regression to build a linear trend model. Comment on the goodness-of-fit of this model to the data (or, how well does R2 explain the variance in the data?). Plot the predictions from this model on the graph with the original data.
Develop multiplicative seasonal indices for the linear trend model developed in question 3. Use these indices to adjust predictions from the linear trend model from question 3 above 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 next 12 months of 1997 using this technique.
Which forecasting method of those that you tried do you have the most confidence for making accurate forecasts for 1997? Use MAPE (mean absolute percent error) as your criterion to justify your decision.
Enrichment : Use Optimization (and Solver in Excel) to find the optimal smoothing constant in problem 2 above (by minimizing the Mean Squared Error or MSE).
Case Study 2: 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 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 measure in dollars, but scaled according to some standard. By the late 1980’s, for example, the scale was based on numbers around 100, with 100 representing the average box-office return of 1980. The figures from 1987 and 1996 are given in the table below and in the file BoxOffice.xlsx in blackboard.
All the figures are scaled around the 1980’s box-office returns, but instead of dollars, artificial numbers are used. Film executives can get a relative indication of the box-office figures compared to the arbitrary 1980 scale. For example, in January 1987 the box-office returns to the film industry were 95% of the average that year, whereas in January 1988 the returns were 104% of the average of 1980 (or, they were 4% above the average of 1980’s figure).
Month
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
Jan
95
104
101
88
132
125
111
127
119
147
Feb
94
100
96
110
109
118
123
129
147
146
Mar
98
99
82
129
101
121
121
132
164
133
Apr
96
88
84
113
111
140
139
108
135
148
May
95
89
85
114
140
141
119
115
124
141
Jun
115
108
124
169
179
201
156
149
168
191
Jul
107
109
134
131
145
152
154
155
159
178
Aug
104
101
109
139
140
138
136
129
137
156
Sep
96
106
121
120
120
137
105
117
149
119
Oct
112
102
111
115
129
138
132
166
159
138
Nov
98
78
101
116
118
144
123
152
175
175
Dec
102
111
112
128
139
148
164
173
195
188
From the time series given in the above table, you will make a forecast for the 12 months of the next year, 1997.
Managerial Report is due on … Friday, 24 Sept
Produce a time series plot of the data. From this graph, do you see a pattern? Can you see any seasonality in the data?
Use exponential smoothing to fit the data. Select an appropriate constant α based on the variation you see in the data. Comment on the appropriateness of exponential smoothing on this data set. Plot the predictions from this model on the graph with the original data. How well does this technique fit the data? Make forecasts for 1997.
Use regression to build a linear trend model. Comment on the goodness-of-fit of this model to the data (or, how well does R2 explain the variance in the data?). Plot the predictions from this model on the graph with the original data.
Develop multiplicative seasonal indices for the linear trend model developed in question 3. Use these indices to adjust predictions from the linear trend model from question 3 above 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 next 12 months of 1997 using this technique.
Which forecasting method of those that you tried do you have the most confidence for making accurate forecasts for 1997? Use MAPE (mean absolute percent error) as your criterion to justify your decision.
Enrichment : Use Optimization (and Solver in Excel) to find the optimal smoothing constant in problem 2 above (by minimizing the Mean Squared Error or MSE).