Asymptotically honest fiducial generalized inference: an application in autoregressive models

Abstract

This paper firstly studies the coefficients estimation of the AR model with normal innovation by proposing an asymptotically honest generalized fiducial (AHGF) method. Furthermore, the AHGF method is introduced to skew-normal setting. Simulation results show that the AHGF method shows more advantages than traditional methods. Specifically, the AHGF method often has a smaller mean square error for point estimation. And for interval estimation, the AHGF method behaves closer to the nominal level than other methods while maintaining comparable or shorter lengths. Finally, a temperature dataset and a sunspot series are applied to illustrate the proposed AHGF methodology.

Keywords:

• Autoregressive model
• asymptotically honest generalized fiducial method
• point estimation
• confidence interval

Disclosure statement

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

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 12001155], and the Natural Science Foundation of Hebei Province [grant numbers A2020207006 and A2022208001].