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December 2014 Functional response additive model estimation with online virtual stock markets
Yingying Fan, Natasha Foutz, Gareth M. James, Wolfgang Jank
Ann. Appl. Stat. 8(4): 2435-2460 (December 2014). DOI: 10.1214/14-AOAS781

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.

Citation

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Yingying Fan. Natasha Foutz. Gareth M. James. Wolfgang Jank. "Functional response additive model estimation with online virtual stock markets." Ann. Appl. Stat. 8 (4) 2435 - 2460, December 2014. https://doi.org/10.1214/14-AOAS781

Information

Published: December 2014
First available in Project Euclid: 19 December 2014

zbMATH: 06408785
MathSciNet: MR3292504
Digital Object Identifier: 10.1214/14-AOAS781

Keywords: forecasting , functional data , Hollywood , movies , Nonlinear regression , penalty functions , virtual markets

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.8 • No. 4 • December 2014
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