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Title: Multiple non-crossing quantiles models for density forecasting Authors:  Mauro Bernardi - University of Padova (Italy) [presenting]
Francesco Lisi - University of Padova (Italy)
Abstract: Traditional quantile regression methods aim at modeling the conditional quantile of a response variable given a set of covariates and a given confidence level, thereby ignoring relevant information coming from adjacent quantiles. Information from multiple quantile estimates is usually combined ``a posteriori'' providing a complete picture of the conditional response. However, results of multiple comparisons of individual quantile estimates can be misleading whenever quantile curves cross each other. Recently, a few alternative approaches have been proposed to deal with the joint estimation of multiple quantile curves imposing non-crossing quantile conditions. We address this issue by taking advantage of a convenient Gaussian Markov random field (GMRF) representation of a penalty term acting on the multiple quantile loss function. In this way, we are able to straightforwardly incorporate dependence in the multiple quantile process. Theoretical properties of the process are investigated and an efficient algorithm for dealing with high-dimensional semi-parametric regression is provided. We show the effectiveness and the advantages of incorporating prior dependence into the multiple conditional quantile process by applying it to a data set of renewable energy productions with the goal of providing density forecasting measures of the production by means of semi-parametric additive models.