Journal of Computations & Modelling

Non-parametric Estimation of Conditional Quantile Functions for AR(1)-ARCH(1) Processes

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  • Abstract

    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. 

    Mathematics Subject Classification: 62G07; 62G05; 62G20; 62G35; 62G30
    Keywords: Prediction; Conditional Quantile; Convergence; Kernel Distribution Estimation; Quantile Autoregression; Heteroscedasticity; Inversion