In this paper,
non-parametric estimations of conditional quantile functions for time series
with AR(1)-ARCH(1) scheme are carried out. An algorithm to estimating two
quantile functions robustly is proposed and a use of a prediction method for
non-parametric conditional quantile regression was adopted to deal with the
problem of boundary effects due to outliers. Our estimations are proven to be
more accurate than the existing and very simple to compute. An overview of the
data generating process is given to ascerntain stationaruty of the process. All
the estimations were based on the quantile regression method by Koenker and
Zaho using the minimization of the conditional expectation of a loss function.
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