Open Access
2024 Robust inference in AR-G/GARCH models under model uncertainty
Shang-Yuan Shiu, Hsin-Chieh Wong
Author Affiliations +
Electron. J. Statist. 18(1): 1970-2020 (2024). DOI: 10.1214/24-EJS2244


This paper provides a robust test for a function of the autoregressive parameters in AR models driven by G/GARCH noise under model uncertainty in an asymptotic framework. To address this method, we adopt the model average and choose weights based on our Mallows-type methods. We next present a valid confidence interval by dividing the sample into a fixed number of groups to form a normalized estimator which is asymptotically related to the Student’s t-distribution. We derive asymptotic results that are not only interesting in their own right, but contribute to the theoretical foundations. These results include limiting distributions of the proposed Mallows-type model averaging and selection estimators. The proposed averaging estimators are stable-family distributions and are yet to be precisely characterized; hence they cannot be implemented by simulation. Through simulation experiments, our method yields outstanding numerical performance, especially for testing the quotient of coefficients in finite-sample tests.

Funding Statement

Shang-Yuan Shiu appreciates the financial support provided by grants MOST 109-2115-M-008-006-MY2 and MOST 111-2115-M-008-005-MY2 of the National Science and Technology Council, Taiwan. Hsin-Chieh Wong appreciates the financial support partially provided by grants NSTC 111-2118-M-305-004-MY2 of the National Science and Technology Council, Taiwan and 112-NTPU ORDA-F-003 of National Taipei University, Taiwan. Hsin-Chieh Wong would also like to thank the University Social Responsibility Program (2023–2024 program), “Promoting a Sustainable Low-Carbon Economic Living Circle in Sanxia-Yingge Area” by the Ministry of Education sponsorship to National Taipei University, for funds supporting this research.


We are thankful for the invaluable suggestions of the associate editor and editors of Electronic Journal of Statistics.


Download Citation

Shang-Yuan Shiu. Hsin-Chieh Wong. "Robust inference in AR-G/GARCH models under model uncertainty." Electron. J. Statist. 18 (1) 1970 - 2020, 2024.


Received: 1 June 2022; Published: 2024
First available in Project Euclid: 29 April 2024

Digital Object Identifier: 10.1214/24-EJS2244

Primary: 62F03 , 62M10
Secondary: 62F12

Keywords: AR-G/GARCH , heavy tails , Mallows-type criteria , model averaging , Model selection , stable distribution , tail behavior

Vol.18 • No. 1 • 2024
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