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While functional regression models have received increasing attentionrecently, most existing approaches assume both a linear relationship and ascalar response variable. We suggest a new method, "Functional ResponseAdditive Model Estimation" (FRAME), which extends the usual linear regressionmodel to situations involving both functional predictors, $X_j(t)$, scalarpredictors, $Z_k$, and functional responses, $Y(s)$. Our approach uses apenalized least squares optimization criterion to automatically performvariable selection in situations involving multiple functional and scalarpredictors. In addition, our method uses an efficient coordinate descentalgorithm to fit general nonlinear additive relationships between thepredictors and response. We develop our model for novel forecasting challengesin the entertainment industry. In particular, we set out to model the decayrate of demand for Hollywood movies using the predictive power of onlinevirtual stock markets (VSMs). VSMs are online communities that, in amarket-like fashion, gather the crowds' prediction about demand for aparticular product. Our fully functional model captures the pattern ofpre-release VSM trading prices and provides superior predictive accuracy of amovie's post-release demand in comparison to traditional methods. In addition,we propose graphical tools which give a glimpse into the causal relationshipbetween market behavior and box office revenue patterns, and hence providevaluable insight to movie decision makers.

Functional response additive model estimation with online virtual stock markets