Multivariate functional linear regression and prediction

Jeng-Min Chiou, Ya-Fang Yang and Yu-Ting Chen

Journal of Multivariate Analysis, 2016, vol. 146, issue C, 301-312

Abstract: We propose a multivariate functional linear regression (mFLR) approach to analysis and prediction of multivariate functional data in cases in which both the response and predictor variables contain multivariate random functions. The mFLR model, coupled with the multivariate functional principal component analysis approach, takes the advantage of cross-correlation between component functions within the multivariate response and predictor variables, respectively. The estimate of the matrix of bivariate regression functions is consistent in the sense of the multi-dimensional Gram–Schmidt norm and is asymptotically normally distributed. The prediction intervals of the multivariate random trajectories are available for predictive inference. We show the finite sample performance of mFLR by a simulation study and illustrate the method through predicting multivariate traffic flow trajectories for up-to-date and partially observed traffic streams.

Keywords: Functional prediction; Functional principal component analysis; Functional regression; Multivariate functional data; Stochastic processes (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (20)

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DOI: 10.1016/j.jmva.2015.10.003

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