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Simultaneous inference of linear models with time varying coefficients

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  • Zhou Zhou
  • Wei Biao Wu

Abstract

Summary. The paper considers construction of simultaneous confidence tubes for time varying regression coefficients in functional linear models. Using a Gaussian approximation result for non‐stationary multiple time series, we show that the constructed simultaneous confidence tubes have asymptotically correct nominal coverage probabilities. Our results are applied to the problem of testing whether the regression coefficients are of certain parametric forms, which is a fundamental problem in the inference of functional linear models. As an application, we analyse an environmental data set and study the association between levels of pollutants and hospital admissions.

Suggested Citation

  • Zhou Zhou & Wei Biao Wu, 2010. "Simultaneous inference of linear models with time varying coefficients," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 513-531, September.
    • Handle: RePEc:bla:jorssb:v:72:y:2010:i:4:p:513-531
    DOI: 10.1111/j.1467-9868.2010.00743.x
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    Cited by:

    1. Cai, Zongwu & Juhl, Ted, 2023. "The distribution of rolling regression estimators," Journal of Econometrics, Elsevier, vol. 235(2), pages 1447-1463.
    2. Holger Dette & Subhra Sankar Dhar & Weichi Wu, 2021. "Identifying shifts between two regression curves," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 855-889, October.
    3. Jiti Gao & Bin Peng & Wei Biao Wu & Yayi Yan, 2022. "Time-Varying Multivariate Causal Processes," Papers 2206.00409, arXiv.org.
    4. Jiaqi Li & Likai Chen & Kun Ho Kim & Tianwei Zhou, 2022. "Simultaneous Inference of a Partially Linear Model in Time Series," Papers 2212.10359, arXiv.org, revised Sep 2023.
    5. Ngai Hang Chan & Linhao Gao & Wilfredo Palma, 2022. "Simultaneous variable selection and structural identification for time‐varying coefficient models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(4), pages 511-531, July.
    6. Karmakar, Sayar & Richter, Stefan & Wu, Wei Biao, 2022. "Simultaneous inference for time-varying models," Journal of Econometrics, Elsevier, vol. 227(2), pages 408-428.
    7. Zhang, Ting, 2015. "Semiparametric model building for regression models with time-varying parameters," Journal of Econometrics, Elsevier, vol. 187(1), pages 189-200.
    8. Lujia Bai & Weichi Wu, 2021. "Detecting long-range dependence for time-varying linear models," Papers 2110.08089, arXiv.org, revised Mar 2023.
    9. Li, Degui & Phillips, Peter C.B. & Gao, Jiti, 2020. "Kernel-based Inference in Time-Varying Coefficient Cointegrating Regression," Journal of Econometrics, Elsevier, vol. 215(2), pages 607-632.
    10. Zongwu Cai & Ted Juhl, 2020. "The Distribution Of Rolling Regression Estimators," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202218, University of Kansas, Department of Economics, revised Dec 2022.
    11. Jiti Gao & Bin Peng & Wei Biao Wu & Yayi Yan, 2022. "Time-Varying Multivariate Causal Processes," Monash Econometrics and Business Statistics Working Papers 8/22, Monash University, Department of Econometrics and Business Statistics.
    12. Kim, Kun Ho & Kim, Taejin, 2016. "Capital asset pricing model: A time-varying volatility approach," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 268-281.
    13. Baillie, Richard T. & Kim, Kun Ho, 2015. "Was it risk? Or was it fundamentals? Explaining excess currency returns with kernel smoothed regressions," Journal of Empirical Finance, Elsevier, vol. 34(C), pages 99-111.
    14. Čížek, Pavel & Koo, Chao Hui, 2021. "Jump-preserving varying-coefficient models for nonlinear time series," Econometrics and Statistics, Elsevier, vol. 19(C), pages 58-96.
    15. Zhou Zhou, 2013. "Inference for non-stationary time-series autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 508-516, July.
    16. Weichi Wu & Zhou Zhou, 2017. "Nonparametric Inference for Time-Varying Coefficient Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 98-109, January.
    17. 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.
    18. Li Cai & Suojin Wang, 2021. "Global statistical inference for the difference between two regression mean curves with covariates possibly partially missing," Statistical Papers, Springer, vol. 62(6), pages 2573-2602, December.
    19. Holger Dette & Weichi Wu, 2020. "Prediction in locally stationary time series," Papers 2001.00419, arXiv.org, revised Jan 2020.
    20. Ok, Hyunmin & Kim, Jinyong & Kim, Yongsik, 2023. "Is the Kimchi premium a speculative bubble?," Finance Research Letters, Elsevier, vol. 57(C).
    21. Guanqun Cao & Lijian Yang & David Todem, 2012. "Simultaneous inference for the mean function based on dense functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 359-377.
    22. Hu, Lixia & Huang, Tao & You, Jinhong, 2019. "Two-step estimation of time-varying additive model for locally stationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 130(C), pages 94-110.
    23. 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.
    24. Xingcai Zhou & Guang Yang & Yu Xiang, 2022. "Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models," Mathematics, MDPI, vol. 10(13), pages 1-15, July.

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