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.)

Least absolute deviations estimation for nonstationary vector autoregressive time series models with pure unit roots

Pages: 199 – 216



Yao Zheng (Department of Statistics, University of Connecticut, Storrs, Conn., U.S.A.)

Jianhong Wu (Department of Mathematics, Shanghai Normal University, Shanghai, China)

Wai Keung Li (Department of Mathematics & Information Technology, Education University of Hong Kong)

Guodong Li (Department of Statistics & Actuarial Science, University of Hong Kong)


This paper derives the asymptotic distribution of the least absolute deviations estimator for nonstationary vector autoregressive time series models with pure unit roots under mild conditions. As this distribution has a complicated form, many commonly used bootstrap techniques cannot be directly applied. To tackle this problem, we propose a novel hybrid bootstrap method by combining the classical wild bootstrap and the method in [17]. We establish the asymptotic validity of the proposed method and further apply it to construct three bootstrapping panel unit root tests. Monte Carlo experiments support the validity of our inference procedure in finite samples. The usefulness of the proposed panel unit root tests is demonstrated via analyses of real economic and financial data sets.


Bootstrap, least absolute deviations; panel unit root test; vector autoregression

2010 Mathematics Subject Classification

Primary 62F40, 62H15, 91B84. Secondary 62F35.

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The authors were partially supported by the National Nature Science Foundation of China (72173086 and 72033002), and by Hong Kong RGC grant 17306519.

Received 1 March 2021

Accepted 27 December 2021

Published 13 April 2023