Functional principal component analysis of quantile curves

Literature on functional data analysis  is mainly focused on estimation of individuals curves and characterization of average dynamics. The idea underlying this proposal is to focus attention on other particular features of the distribution of the observed data, moving from mean functions towards functional  quantiles. The motivating examples are functional data sets that are collections of high frequency data recorded along time. As quantiles provide information on various aspects of a time series, we propose a modelling framework for the joint estimation of functional quantiles, varying along time, and  functional  principal components, summarizing  some common dynamics shared by the functional quantiles.