Abstract:
In this thesis, we carried out the estimation smoothed Conditional Scale Function for an
Autoregressive process with conditional heteroscedastic innovations by using the kernel
smoothing approach. The estimations were based on the quantile Auregression methodology
proposed by Koenker and Bassett. The proof of the asymptotic properties was
given. All our estimations were made through inverting conditional distribution functions
and we showed that they are weakly consistent under specific assumptions. We
performed Monte Carlo studies to show the accuracy of our estimators. This study can
use in area requiring conditional quantile estimations can be improve using local polynomial
estimation of degree two.
