  This paper proposes a model-free nonparametric estimator of conditional
quantile of a time series regression model where the covariate vector is
repeated many times for different values of the response. This type of data is
abound in climate studies. To tackle such problems, our proposed method
exploits the replicated nature of the data and improves on restrictive linear
model structure of conventional quantile regression. Relevant asymptotic theory
for the nonparametric estimators of the mean and variance function of the model
are derived under a very general framework. We provide a detailed simulation
study which clearly demonstrates the gain in efficiency of the proposed method
over other benchmark models, especially when the true data generating process
entails nonlinear mean function and heteroskedastic pattern with time dependent
covariates. The predictive accuracy of the non-parametric method is remarkably
high compared to other methods when attention is on the higher quantiles of the
variable of interest. Usefulness of the proposed method is then illustrated
with two climatological applications, one with a well-known tropical cyclone
wind-speed data and the other with an air pollution data.
