High dimensional regression for regenerative time-series: an application to road traffic modeling

This paper investigates statistical models for road traffic modeling. The proposed methodology considers road traffic as a (i) highdimensional time-series for which (ii) regeneration occurs at the end of each day. Since (ii), prediction is based on a daily modeling of the road traffic using a vector autoregressive model that combines linearly the past observations of the day. Considering (i), the learning algorithm follows from an l1-penalization of the regression coefficients. Excess risk bounds are established under the high-dimensional framework in which the number of road sections goes to infinity with the number of observed days. Considering floating car data observed in an urban area, the approach is compared to state-of-the-art methods including neural networks. In addition of being very competitive in terms of prediction, it enables to identify the most determinant sections of the road network.