  We propose a nonparametric method for estimating the conditional quantile
function that admits a generalized additive specification with an unknown link
function. This model nests single-index, additive, and multiplicative quantile
regression models. Based on a full local linear polynomial expansion, we first
obtain the asymptotic representation for the proposed quantile estimator for
each additive component. Then, the link function is estimated by noting that it
corresponds to the conditional quantile function of a response variable given
the sum of all additive components. The observations are supposed to be a
sample from a strictly stationary and absolutely regular process. We provide
results on (uniform) consistency rates, second order asymptotic expansions and
point wise asymptotic normality of each proposed estimator.
