Beyond Opening Weekend: Hidden Markov States in Weekly Box Office Dynamics

Abstract

This thesis introduces a dynamic framework for analyzing how films progress in the box office by implementing a Hidden Markov Model that interprets hidden states as ordered revenue tiers. Past studies forecast the financial success of a film based on prerelease signals and opening weekend revenue streams, but they do not account for the full theatrical trajectory and thus overlook valuable, time-dependent information. Therefore, this thesis takes an exploratory approach, not a predictive one, to modeling weekly box office revenue streams over the entire theatrical run of a film. Using a dataset containing 5,280 domestic films with varying genres, production budgets, total box office grosses, and more, we seek to uncover how hidden revenue states relate to financial outcomes. Films that have been rereleased have separate box office trajectories, and the data is pre-processed to account for seasonality effects. Selection and validation are performed to choose an effective number of K states for the model. Then, we fit a 15-state HMM to decode hidden revenue state assignments, and relate the fractional share of each state back to financial metrics including domestic ROI and total box office through grouped comparisons and cross-sectional regressions. Results indicate that films with high ROI or large box office tend to have lasting persistence in the high and upper middle revenue states, while films with low ROI or small box office spend more time in the low revenue state. Overall, this thesis provides intriguing results that align well with common expectations, but more importantly it reveals the significance of analyzing the entire dynamic trajectory of a film in the box office.