BAYESIAN ESTIMATION OF QUANTILE REGRESION MODELS IN THE PRESENCE OF AUTOCORRELATION

Abstract

The principal goal of this work is the estimation of regression quantiles in the presence of autocorrelation from a Bayesian point of view. Regression models are based on several important statistical assumptions upon which their inferences rely upon. Autocorrelation of the error terms violates the ordinary least squares regression assumptions that the error terms are uncorrelated, they no longer have the minimum variance property, and also invalidate Gauss Markov theorem. Regression quantiles provides estimates for regression models fit to any part of a response distribution and require minimal assumptions about the form of error distribution. Quantile regression is a comprehensive approach to the statistical analysis of linear and nonlinear response models, it has a strong link to three useful statistical concepts- regression, robustness and extreme value theory. This research developed an adaptive Bayesian Markov Chain Monte Carlo scheme that explored the interaction between causality quantile regression models and skew Laplace distribution. The scheme was designed for estimation and making inference of regression quantiles in the presence of auto correlation. The research employed a likelihood –based approach in determining the causality effect of a Bayesian quantile regression model parameter estimates in the presence of autocorrelated error. This work is applied empirically in determining the causality quantile range some relations among export rate, import rate, inflation rate, exchange rate and gross domestic product(GDP), both the simulation studies and the empirical analysis indicate that the proposed method performs well in comparison to the other existing methods. The thesis concludes that while underlying errors are correlated, Bayesian estimates of regression quantiles still provide a less biased and precise estimates.