Statistics and Its Interface

Volume 16 (2023)

Number 2

Special issue on recent developments in complex time series analysis – Part II

Guest editors: Robert T. Krafty (Emory Univ.), Guodong Li (Univ. of Hong Kong), Anatoly Zhigljavsky (Cardiff Univ.)

Empirical likelihood-based portmanteau tests for autoregressive moving average models with possible infinite variance innovations

Pages: 337 – 347



Xiaohui Liu (School of Statistics & Laboratory of Data Science in Finance and Economics, Jiangxi University of Finance and Economics, Nanchang, Jiangxi, China)

Donghui Fan (School of Statistics, Jiangxi University of Finance and Economics, Nanchang, Jiangxi, China)

Xu Zhang (School of Mathematical Sciences, South China Normal University, Guangzhou, China)

Catherine Liu (Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong)


It is an important task in the literature to check whether a fitted autoregressive moving average (ARMA) model is adequate, while the currently used tests may suffer from the size distortion problem when the underlying autoregressive models have low persistence. To fill this gap, this paper proposes two empirical likelihood-based portmanteau tests. The first one is naive but can serve as a benchmark, and the second is for the case with infinite variance innovations. The asymptotic distributions under the null hypothesis are derived under mild moment conditions, and their usefulness is demonstrated by simulation experiments and two real data examples.


ARMA model, GARCH process, diagnostic checking, empirical likelihood, infinite variance

Xiaohui Liu’s research is supported by NSF of China (Grant No.11971208), National Social Science Foundation of China (21&ZD152).

Xu Zhang’s research is supported by NSF of China (Grant No.12171167).

Catherine Liu’s research is partially supported by General Research Funding 15301519, RGC, HKSAR.

Received 16 February 2022

Accepted 22 September 2022

Published 13 April 2023