Functional response additive model estimation with online virtual stock markets

TL;DR

This paper introduces FRAME, a flexible functional response additive model that incorporates multiple predictors and applies it to forecast movie demand using online virtual stock market data, outperforming traditional methods.

Contribution

The paper develops a novel nonlinear additive modeling approach for functional and scalar predictors, with automatic variable selection, applied to entertainment industry forecasting.

Findings

FRAME achieves superior predictive accuracy over traditional methods.

The model captures complex relationships between VSM trading prices and movie demand.

Graphical tools reveal insights into causal links between market behavior and revenue.

Abstract

While functional regression models have received increasing attention recently, most existing approaches assume both a linear relationship and a scalar response variable. We suggest a new method, "Functional Response Additive Model Estimation" (FRAME), which extends the usual linear regression model to situations involving both functional predictors, $X_j(t)$, scalar predictors, $Z_k$, and functional responses, $Y(s)$. Our approach uses a penalized least squares optimization criterion to automatically perform variable selection in situations involving multiple functional and scalar predictors. In addition, our method uses an efficient coordinate descent algorithm to fit general nonlinear additive relationships between the predictors and response. We develop our model for novel forecasting challenges in the entertainment industry. In particular, we set out to model the decay rate of demand for Hollywood movies using the predictive power of online virtual stock markets (VSMs). VSMs are online communities that, in a market-like fashion, gather the crowds' prediction about demand for a particular product. Our fully functional model captures the pattern of pre-release VSM trading prices and provides superior predictive accuracy of a movie's post-release demand in comparison to traditional methods. In addition, we propose graphical tools which give a glimpse into the causal relationship between market behavior and box office revenue patterns, and hence provide valuable insight to movie decision makers.