Two main approaches are usually used to estimate extreme conditional quantiles in nonstationary settings. The first method incorporates the covariates into the parameters of the distribution function of the response variable, and the second method is the quantile regression. However, these two methods cannot fully describe the dependence between the variable of interest and its covariates. In order to overcome this limitation, in addition to dealing with nonstationarity, we propose a copula-based estimator for conditional quantiles. The idea of using copula-based estimators is not new but considering the nonstationary case raises methodological challenges. In particular, we study both the asymptotic behaviour of the estimation errors and the conditional quantiles, and we suggest a bootstrap procedure in order to construct uniform confidence bands around the conditional quantile function. As a by-product, we also obtain a formal goodness-of-fit test. Finally we present a simulation study demonstrating the finite sample performance of the proposed estimator and we illustrate its usefulness with applications to hydro-climatology and finance.
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