Bayesian quantile inference and order shrinkage for hysteretic quantile autoregressive models

Abstract

Hysteretic quantile autoregressive model combines the hysteretic patterns and quantile autoregression, which can capture the dynamic relationship and nonlinear characteristics at different quantiles in time series data. In this paper, the Bayesian quantile inference and order shrinkage are studied for a class of hysteretic quantile autoregressive time series models. By using Markov Chain Monte Carlo (MCMC) techniques, the proposed Bayesian quantile method can handle the sparse hysteretic quantile autoregressive model well. It can accurately determine order of the model and estimate non-zero coefficients. Both simulation studies and a data example show that the proposed methods are feasible, reliable and appropriate for analysing the US Gross National Product data set.

Keywords:

• Quantile autoregression
• hysteretic autoregressive models
• Bayesian quantile inference
• spike-and-slab prior
• order shrinkage

Acknowledgments

We gratefully acknowledge the anonymous reviewers for their careful work and thoughtful suggestions that have helped improve this article substantially.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Social Science Foundation of China [grant number 23BTJ047].