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A Unit Root Test for an AR(1) Process with AR Errors by Using Random Weighted Bootstrap

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Abstract

A great deal of economic problems are related to detecting the stability of time series data, where the main interest is in the unit root test. In this paper, we consider the unit root testing problem with errors being long-memory processes with the GARCH structure. A new test statistic is developed by using the random weighted bootstrap method. It turns out that the proposed statistic has a chi-squared distribution asymptotically regardless of the process being stationary or nonstationary, and with or without an intercept term. The simulation results show that the statistic has a desired finite sample performance in terms of both size and power. A real data application is also given relying on the inflation rate data of 17 countries.

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Acknowledgements

We thank one referee and the Associate Editor for their insightful comments which led to many improvements to this paper.

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Authors and Affiliations

  1. School of Statistics and Data Science, Jiangxi University of Finance and Economics, Nanchang, 330013, P. R. China

    Xiao Hui Liu, Ya Wen Fan, Yu Zi Liu & Shi Hua Luo

  2. Key Laboratory of Data Science in Finance and Economics, Jiangxi University of Finance and Economics, Nanchang, 330013, P. R. China

    Xiao Hui Liu, Ya Wen Fan, Yu Zi Liu & Shi Hua Luo

Authors
  1. Xiao Hui Liu
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  2. Ya Wen Fan
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  3. Yu Zi Liu
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  4. Shi Hua Luo
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Correspondence to Ya Wen Fan.

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The authors declare no conflict of interest.

Additional information

Xiaohui Liu’s research is supported by the NNSF of China (Grant Nos. 11971208 and 11601197), the Outstanding Youth Fund Project of the Science and Technology Department of Jiangxi Province (Grant No. 20224ACB211003). Yawen Fan’s research is supported by the Science and Technology Research Project of Education Department of Jiangxi Province (Grant No. GJJ200545), the Postgraduate Innovation Project of Jiangxi Province (Grant No. YC2021-B124), and NSSF of China (Grant No. 21BTJ035). Shihua Luo’s research is supported by the National Major Social Science Project of China (Grant No. 21&ZD152), the NNSF of China (Grant No. 61973145) and Natural Science Project of Jiangxi Provincial Department of Science and Technology (Grant No. jxsq2023201048)

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Liu, X.H., Fan, Y.W., Liu, Y.Z. et al. A Unit Root Test for an AR(1) Process with AR Errors by Using Random Weighted Bootstrap. Acta. Math. Sin.-English Ser. 39, 1834–1854 (2023). https://doi.org/10.1007/s10114-023-1535-x

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  • DOI: https://doi.org/10.1007/s10114-023-1535-x

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