Asymmetric exponential power Bayesian median autoregression with applications

Abstract

Compared with the widely used mean-based models, the prediction based on median autoregression is often more robust for time series forecasting. Motivated by the asymmetric exponential power working likelihood approach in Bayesian quantile regression, we first apply the asymmetric exponential power error to time series. The new median autoregression we proposed is more robust and can better deal with outliers. An adaptive independent Metropolis-Hastings algorithm is used for the parameter estimation. A novel, simple, and effective approximate forecasting procedure is proposed based on the Watanabe-Akaike information criterion in the framework of Bayesian model averaging. Model assessment, order selection, and out-of-sample predictive accuracy are all discussed. Finally, three examples of macroeconomic data are analyzed to show the superior performance of the proposed model.

Keywords:

• Asymmetric exponential power distribution
• Bayesian model averaging
• median autoregression

Mathematics Subject Classifications:

• 62M10
• 62F15

Acknowledgements

We are deeply grateful to the Editor and two anonymous referees for their careful reading, valuable comments, and constructive suggestions that have improved the revision considerably.

Disclosure statement

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

Notes

1 M2 consists of all M1 (and all M0), savings deposits, and certificates of deposit. M0 refers to currency in circulation, such as coins and cash. M1 includes M0, demand deposits, such as checking accounts, traveller's checks, and currency that is not in circulation but readily available.

Additional information

Funding

Liu's work is supported by the Research Start-up Fund of Nanjing Normal University (No. 184080H202B339) and the Natural Science Foundation of Jiangsu Province Colleges (No. 22KJD110002). Zhu's work is supported by the National Natural Science Foundation of China (No. 12271206), and the Science and Technology Research Planning Project of Jilin Provincial Department of Education (No. JJKH20231122KJ).