Marketing Science Online Appendix. Pre-release Demand Forecasting for Motion Pictures Using Functional Shape Analysis of Virtual Stock Markets

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1 Marketing Science Online Appendix Pre-release Demand Forecasting for Motion Pictures Using Functional Shape Analysis of Virtual Stock Markets Natasha Foutz and Wolfgang Jank Online Appendix 1: Hollywood Marketing Decisions in Weeks Leading to Opening Weekend Online Appendix 2: Robustness of Our Choice of Smoothing Parameter Value (λ = 50) vs. Other Possible Values (λ = 1, 5, 500, 5000) 1

2 Online Appendix 3: Model Comparison: Distribution of Absolute Percentage Errors (APEs) When Forecasting Opening Weekend Revenues Model Description MAPE % Movies Whose APE Is Within: (%) 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 500% >500% A1 Movie Features A2 Movie Features + Ad B1 Latest Price B2 Latest Price + Movie Features B3 Latest Price + Movie Features + Ad C1 4 Shapes C2 2 Path Shapes, No Dynamics C3 All 13 Shapes C4 4 Shapes + Movie Features C5 4 Shapes + Ad C6 4 Shapes + Movie Features + Ad C7 4 Shapes + Latest Price D1 Avg D2 Volume Weighted Avg D3 Median D4 Avg. + Linear D5 Avg. + Linear + Nonlinear E1 Avg. + End.Early + Late Spurt + Early Spurt E2 CART on All 13 Shapes E3 GAM on All 13 Shapes E4 CART on 4 Shapes E5 GAM on 4 Shapes Additional Models*: A3 Movie Features + Screen A4 Movie Features + Audience Rating A5 Movie Features + Audience Rating + Volume of Audience Rating A6 Audience Rating A7 Audience Rating + Volume of Critics Rating + Volume of Audience Rating A8 Movie Features + Oscar + Critics Rating + Audience Rating + Volume of Critics Rating + Volume of Audience Rating A9 Movie Features + Screen + Oscar + Critics Rating + Audience Rating + Volume of Critics Rating + Volume of Audience Rating * The audience ratings were collected from Movies.Yahoo.com and critics ratings from RottenTomatoes.com (Liu 2006; Dellarocas, Zhang, and Awad 2007). Oscars were collected from Oscars.org and coded as 1 if a movie won in one of the following major categories: best picture, best director, best actor, best actress, best supporting actor, and best supporting actress. The results show that augmenting movie features with these additional covariates generally improves the forecast accuracy, but not sufficiently to outperform the proposed Model C1. 2

3 Online Appendix 4: Model Comparison: Distribution of Absolute Percentage Errors (APEs) When Forecasting First-four-weekend Revenues Model Description MAPE % Movies Whose APE Is Within: (%) 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 500% >500% A1 Movie Features A2 Movie Features + Ad B1 Latest Price B2 Latest Price + Movie Features B3 Latest Price + Movie Features + Ad C1 4 Shapes C2 2 Path Shapes, No Dynamics C3 All 13 Shapes C4 4 Shapes + Movie Features C5 4 Shapes + Ad C6 4 Shapes + Movie Features + Ad C7 4 Shapes + Latest Price D1 Avg D2 Volume Weighted Avg D3 Median D4 Avg. + Linear D5 Avg. + Linear + Nonlinear E1 Avg. + End.Early + Late Spurt + Early Spurt E2 CART on All 13 Shapes E3 GAM on All 13 Shapes E4 CART on 4 Shapes E5 GAM on 4 Shapes Additional Models: A3 Movie Features + Screen A4 Movie Features + Audience Rating A5 Movie Features + Audience Rating + Volume of Audience Rating A6 Audience Rating A7 Audience Rating + Volume of Critics Rating + Volume of Audience Rating A8 Movie Features + Oscar + Critics Rating + Audience Rating + Volume of Critics Rating + Volume of Audience Rating A9 Movie Features + Screen + Oscar + Critics Rating + Audience Rating + Volume of Critics Rating + Volume of Audience Rating

4 Online Appendix 5: Forecasting First-four-weekend Revenues Using 4 Shapes Estimate Std. Err. P-Value Intercept P.PC1: Average P.PC2: Early.Late V.PC1: Last-moment Velocity Spurt V.PC2: Early Velocity Spurt The results in Online Appendices 4 and 5 show that when forecasting the first-fourweekend revenues, the early velocity spurts (V.PC2) become less important, although directionally consistent with our earlier results when forecasting the opening weekend revenues. The average price (P.PC1), upward trend (P.PC2), and last-moment velocity spurt (V.PC1) still play important roles. Also, the MAPEs are generally lower across all models when forecasting the first-fourweekend, than opening weekend, revenues. In particular, we notice that the right tails of the error distributions for all models have decreased. As a result, we observe smaller differences in the forecast accuracy across models, although the proposed Model C1 still outperforms almost all alternative models except for E5, suggesting imperfect linearity in the relationship between the revenues and the shapes. Online Appendix 6: Comparison between Proposed Model C1 and Alternative Models in Figure 6 When Forecasting First-four-weekend Revenues MAPE (%) of Alternative Models MAPE (%) of Proposed Model C1 Model Description Week -40 Week -30 Week -20 Week -10 Week 0 A1 Movie Features A2 Movie Features + Ad C6 4 Shapes + Movie Features + Ad B1 Latest Price B3 Latest Price + Movie Features + Ad

5 Online Appendix 7: Bayesian Analysis of Selected Models Model Description Opening Weekend Revenues (MAPE %) First-four-weekend Revenues (MAPE %) A1 Movie Features A2 Movie Features + Ad B1 Latest Price B2 Latest Price + Movie Features B3 Latest Price + Movie Features + Ad D1 Avg D2 Volume Weighted Avg D3 Median D4 Avg.+ Linear D5 Avg. + Linear + Nonlinear E1 Avg. + End.Early + Late Spurt + Early Spurt The results show that the shrinkage-based Bayesian analysis improves upon their frequentist counterparts. Nonetheless, they do not outperform the proposed Model C1. It is also important to note that, from a practical point of view, Bayesian analysis takes longer to complete, and thus if the interest lies with real-time forecasting for dynamic, on-demand decisions, our least-squares approach is advantageous. 5

6 Online Appendix 8: Factors Associated with Higher Forecast Errors When Using Latest Price Alone Estimate Std. Err. P-Value Interaction: Latest Price by Latest Volume MPAA Rating: non-r Week 0 Ad Latest Price To better understand why using the 4 shapes characterizing the price histories (C1), above and beyond the latest prices (B1), improves forecast accuracy, we further regress the gap in the forecast errors between B1 and C1 on the movie features and trading related covariates. We report the significant covariates in the table above. The results show that higher forecast errors from using the latest prices alone are associated with (a) higher latest trading volumes at any given trading price (note the positive interaction between the latest price and volume); (b) non-r rated movies; and (c) higher last-moment advertising effort. In particular, we believe that (a) and (c) result from the last-moment spurts in hype about a movie, which is captured by the shapes, but not quite by the latest prices alone. On the other hand, everything else equal, for movies with higher latest trading prices, which are often widely-interested movies with readily available info accessible to all traders, the latest prices alone may capture more information. Nonetheless, these latest prices immediately before product releases cannot provide the most valuable early forecasts. 6