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Testing for Trends in High-Dimensional Time Series

Author

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  • Likai Chen
  • Wei Biao Wu

Abstract

The article considers statistical inference for trends of high-dimensional time series. Based on a modified L2$\mathcal {L}^2$ distance between parametric and nonparametric trend estimators, we propose a de-diagonalized quadratic form test statistic for testing patterns on trends, such as linear, quadratic, or parallel forms. We develop an asymptotic theory for the test statistic. A Gaussian multiplier testing procedure is proposed and it has an improved finite sample performance. Our testing procedure is applied to a spatial temporal temperature data gathered from various locations across America. A simulation study is also presented to illustrate the performance of our testing method. Supplementary materials for this article are available online.

Suggested Citation

  • Likai Chen & Wei Biao Wu, 2019. "Testing for Trends in High-Dimensional Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 869-881, April.
    • Handle: RePEc:taf:jnlasa:v:114:y:2019:i:526:p:869-881
    DOI: 10.1080/01621459.2018.1456935
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    Cited by:

    1. 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.
    2. 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).
    3. 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.
    4. Khismatullina, Marina & Vogt, Michael, 2023. "Nonparametric comparison of epidemic time trends: The case of COVID-19," Journal of Econometrics, Elsevier, vol. 232(1), pages 87-108.
    5. Marina Khismatullina & Michael Vogt, 2022. "Multiscale Comparison of Nonparametric Trend Curves," Papers 2209.10841, arXiv.org.

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