Functional Response Additive Model Estimation with Online Virtual Stock Markets

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 which extends the usual linear regression model to situations involving both functional responses, Xj(t), and functional predictors, Y (t). Our approach uses a penalized least squares optimization criterion to automatically perform variable selection in situations involving multiple functional predictors. In addition our method uses an efficient coordinate descent algorithm to fit general non-linear additive relationships between the predictors and response. We apply our model to the context of forecasting product demand in the entertainment industry. In particular, we 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’ opinion about a particular product. Our fully functional model captures the pattern of pre-release VSM trading values and provides superior predictive accuracy of a movie’s demand distribution 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.