Bayesian Estimation of Regression Quantiles in the Presence of Autocorrelated Errors

Abstract

This is a study of  Bayesian quantile regression that broadly considered the estimation of regression quantiles in the presence of autocorrelated error. Regression models are based on several important statistical assumptions upon which their inferences rely. Autocorrelation of the error terms violates the ordinary least squares regression assumption that error terms are uncorrelated which invalidate Gauss Markov theorem. This study designed schemes for estimation and making inference of regression quantiles in the presence of autocorrelated errors using Bayesian approach. Bayesian method to quantile regression models regards unknown parameters as random variables and the parameter uncertainty was taken into account without relying on asymptotic approximations.The empirical analysis used  the data set from Central Bank of Nigeria bulletin which comprised of Nigeria GDP growth, export rate, import rate, inflation rate and exchange rate from the period of 1985–2018. Bayesian inferences with autocorrelated error in the framework of quantile regression accounted better for the variability in the distribution of autocorrelation and gave robust and less biased estimates in dealing with non normality and non constant variance assumptions, the results of the research reported minimal Mean Square Errors in Bayesian approach than classical approach across the entire distribution.
 
Keywords: Bayesian Estimation, Regression Quantiles, Autocorrelated Errors, Regression Analysis.