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Inference of trends in time series


  • Wei Biao Wu
  • Zhibiao Zhao


We consider statistical inference of trends in mean non-stationary models. A test statistic is proposed for the existence of structural breaks in trends. On the basis of a strong invariance principle of stationary processes, we construct simultaneous confidence bands with asymptotically correct nominal coverage probabilities. The results are applied to global warming temperature data and Nile river flow data. Our confidence band of the trend of the global warming temperature series supports the claim that the trend is increasing over the last 150 years. Copyright 2007 Royal Statistical Society.

Suggested Citation

  • Wei Biao Wu & Zhibiao Zhao, 2007. "Inference of trends in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 391-410.
  • Handle: RePEc:bla:jorssb:v:69:y:2007:i:3:p:391-410

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    Cited by:

    1. Zhao, Zhibiao & Wu, Wei Biao, 2009. "Nonparametric inference of discretely sampled stable Lévy processes," Journal of Econometrics, Elsevier, vol. 153(1), pages 83-92, November.
    2. Kim, Seonjin & Zhao, Zhibiao & Shao, Xiaofeng, 2015. "Nonparametric functional central limit theorem for time series regression with application to self-normalized confidence interval," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 277-290.
    3. Luis A. Gil-Alana, 2009. "Warming break trends and fractional integration in the northern, southern and global temperature anomaly series," Faculty Working Papers 09/09, School of Economics and Business Administration, University of Navarra.
    4. Shuzhuan Zheng & Rong Liu & Lijian Yang & Wolfgang K. Härdle, 2016. "Statistical inference for generalized additive models: simultaneous confidence corridors and variable selection," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 607-626, December.
    5. Raffaella Giacomini & Barbara Rossi, 2016. "Model Comparisons In Unstable Environments," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57, pages 369-392, May.
    6. Likai Chen & Weining Wang & Wei Biao Wu, 2017. "Dynamic Semiparametric Factor Model with a Common Break," SFB 649 Discussion Papers SFB649DP2017-026, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    7. Shuzhuan Zheng & Rong Liu & Lijian Yang & Wolfgang Karl Härdle, 2014. "Simultaneous Confidence Corridors and Variable Selection for Generalized Additive Models," SFB 649 Discussion Papers SFB649DP2014-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Yujiao Yang & Qiongxia Song, 2014. "Jump detection in time series nonparametric regression models: a polynomial spline approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 325-344, April.
    9. Zhang, Ting, 2015. "Semiparametric model building for regression models with time-varying parameters," Journal of Econometrics, Elsevier, vol. 187(1), pages 189-200.
    10. Zhibiao Zhao & Yiyun Zhang & Runze Li, 2014. "Non-Parametric Estimation Under Strong Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(1), pages 4-15, January.
    11. Markus Bibinger & Moritz Jirak & Mathias Vetter, 2015. "Nonparametric change-point analysis of volatility," SFB 649 Discussion Papers SFB649DP2015-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    12. Jan Mielniczuk & Zhou Zhou & Wei Biao Wu, 2009. "On nonparametric prediction of linear processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(6), pages 652-673, November.
    13. Degras, David, 2008. "Asymptotics for the nonparametric estimation of the mean function of a random process," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2976-2980, December.
    14. Friedrich, Marina & Smeekes, Stephan & Urbain, Jean-Pierre, 2017. "Autoregressive Wild Bootstrap Inference for Nonparametric Trends," Research Memorandum 010, Maastricht University, Graduate School of Business and Economics (GSBE).

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