ESTIMATION OF SMOOTHED CONDITIONAL SCALE FUNCTION USING QUANTILE AUTOREGRESSIVE PROCESS WITH CONDITIONAL HETEROSCEDASTIC INNOVATIONS

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.