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Testing parametric assumptions of trends of a nonstationary time series

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  • Ting Zhang
  • Wei Biao Wu

Abstract

The paper considers testing whether the mean trend of a nonstationary time series is of certain parametric forms. A central limit theorem for the integrated squared error is derived, and a hypothesis-testing procedure is proposed. The method is illustrated in a simulation study, and is applied to assess the mean pattern of lifetime-maximum wind speeds of global tropical cyclones from 1981 to 2006. We also revisit the trend pattern in the central England temperature series. Copyright 2011, Oxford University Press.

Suggested Citation

  • Ting Zhang & Wei Biao Wu, 2011. "Testing parametric assumptions of trends of a nonstationary time series," Biometrika, Biometrika Trust, vol. 98(3), pages 599-614.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:3:p:599-614
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    File URL: http://hdl.handle.net/10.1093/biomet/asr017
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    Citations

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    Cited by:

    1. Marina Friedrich & Eric Beutner & Hanno Reuvers & Stephan Smeekes & Jean-Pierre Urbain & Whitney Bader & Bruno Franco & Bernard Lejeune & Emmanuel Mahieu, 2020. "A statistical analysis of time trends in atmospheric ethane," Climatic Change, Springer, vol. 162(1), pages 105-125, September.
    2. Euan T. McGonigle & Rebecca Killick & Matthew A. Nunes, 2022. "Trend locally stationary wavelet processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(6), pages 895-917, November.
    3. Deshui Yu & Yayi Yan, 2023. "Joint dynamics of stock returns and cash flows: A time‐varying present‐value framework," Financial Management, Financial Management Association International, vol. 52(3), pages 513-541, September.
    4. Degui Li & Bin Peng & Songqiao Tang & Weibiao Wu, 2023. "Inference of Grouped Time-Varying Network Vector Autoregression Models," Monash Econometrics and Business Statistics Working Papers 5/23, Monash University, Department of Econometrics and Business Statistics.
    5. Zhang, Rongmao & Chan, Ngai Hang & Chi, Changxiong, 2023. "Nonparametric testing for the specification of spatial trend functions," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    6. Zhang, Ting, 2015. "Semiparametric model building for regression models with time-varying parameters," Journal of Econometrics, Elsevier, vol. 187(1), pages 189-200.
    7. Xu Guo & Tao Wang & Lixing Zhu, 2016. "Model checking for parametric single-index models: a dimension reduction model-adaptive approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(5), pages 1013-1035, November.
    8. Pei, Youquan & Huang, Tao & You, Jinhong, 2018. "Nonparametric fixed effects model for panel data with locally stationary regressors," Journal of Econometrics, Elsevier, vol. 202(2), pages 286-305.
    9. Erhua Zhang & Xiaojun Song & Jilin Wu, 2022. "A non‐parametric test for multi‐variate trend functions," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(6), pages 856-871, November.
    10. Degui Li & Bin Peng & Songqiao Tang & Weibiao Wu, 2023. "Estimation of Grouped Time-Varying Network Vector Autoregression Models," Papers 2303.10117, arXiv.org, revised Mar 2024.
    11. Yayi Yan & Jiti Gao & Bin Peng, 2021. "Asymptotics for Time-Varying Vector MA(∞) Processes," Monash Econometrics and Business Statistics Working Papers 22/21, Monash University, Department of Econometrics and Business Statistics.

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