Bayesian Weighed Quantile Regression Of Auto-regressive Models

There is a growing literature devoted to Autoregressive(AR)models with finite variance errors.This paper consider AR models with heavy-tailed errors,which is effective in numerous scientific research field.Statistical methods for AR models with infinite variance errors is extremely different from those for AR models with finite variance errors.In this paper,we ponder a weighted quantile regression for AR models to figure out infinite infinite variance errors.Further,we propose a bayesian weighted quantile regression approach with weighted asymmetric Laplace distribution to make it easier to solve computational challenges in weighted quantile regression.We provide the expression of likelihood function with bayesian weighted quantile regression,then extract the posterior distribution using HMC sampling.