Simulation Study of Autocorrelated Error Using Bayesian Quantile Regression

Abstract

 

The purpose of this study is to compare the ability of the Classical Quantile Regression method and the Bayesian Quantile Regression method in estimating models that contain autocorrelated error problems using simulation studies. In the quantile regression approach, the data response is divided into several pieces or quantiles conditions on indicator variables. Then, The parameter model is estimated for each selected quantiles. The parameters are estimated using conditional quantile functions obtained by minimizing absolute asymmetric errors. In the Bayesian quantile regression method, the data error is assumed to be asymmetric Laplace distribution. The Bayesian approach for quantile regression uses the Markov Chain Monte Carlo Method with the Gibbs sample algorithm to produce a converging posterior mean. The best method for estimating parameter is the method that produces the smallest absolute value of bias and the smallest confidence interval. This study resulted that the Bayesian Quantile method produces smaller absolute bias values and confidence intervals than the quantile regression method. These results proved that the Bayesian Quantile Regression method tends to produce better estimate values than the Quantile Regression method in the case of autocorrelation errors.                                                                                                                                                                                    

Keywords: Quantile Regression Method, Bayesian Quantile Regression Method, Confidence Interval, Autocorrelation.