Direct Nonparametric Conditional Quantile and Scale Regression Estimation, with pplication to Financial Time Series Data

Abstract

We consider a nonparametric approach in estimation of conditional quantile andscale functions for _nancial time series at both interior and boundary points. Theestimation combines local linear approximation and the quantile regression method-ology introduced by Koenker and Basset [27]. In particular, we have suggested twoestimators, a direct non-parametric local linear estimator of the conditional quan-tile function vis-_a-vis direct nonparametric local linear estimator of the conditionalscale function. The two estimators are estimated under a quantile-scale model set upwhere the latter is estimated under the assumption that the former is unknown andit has to be estimated _rst. Consistency and asymptotic properties are investigatedand were found to be good at interior and at boundary points. Finally, we havesubjected the estimators to simulated and the results support the theoretical resultsalready established for the proposed estimators.