Functional response additive model estimation with online virtual stock markets

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.

Published in at http://dx.doi.org/10.1214/14-AOAS781 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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• Functional linear regression analysis for longitudinal data
• One-step sparse estimates in nonconcave penalized likelihood models
• Multilevel functional principal component analysis
• Single and multiple index functional regression models with nonparametric link
• Functional additive regression
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Cited by in corpus (7)

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• Review of Functional Data Analysis
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• An autocovariance-based learning framework for high-dimensional functional time series
• Functional Linear Regression with Mixed Predictors
• Finite Sample Theory for High-Dimensional Functional/Scalar Time Series with Applications
• The Function-on-Scalar LASSO with Applications to Longitudinal GWAS