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Inference of trends in time series


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  • 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.

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Bibliographic Info

Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).

Volume (Year): 69 (2007)
Issue (Month): 3 ()
Pages: 391-410

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Handle: RePEc:bla:jorssb:v:69:y:2007:i:3:p:391-410

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Cited by:
  1. Luis A. Gil-Alana, 2009. "Warming break trends and fractional integration in the northern, southern and global temperature anomaly series," Faculty Working Papers, School of Economics and Business Administration, University of Navarra 09/09, School of Economics and Business Administration, University of Navarra.
  2. Zhao, Zhibiao & Wu, Wei Biao, 2009. "Nonparametric inference of discretely sampled stable Lévy processes," Journal of Econometrics, Elsevier, Elsevier, vol. 153(1), pages 83-92, November.
  3. Raffaella Giacomini & Barbara Rossi, 2012. "Model comparisons in unstable environments," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP13/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Degras, David, 2008. "Asymptotics for the nonparametric estimation of the mean function of a random process," Statistics & Probability Letters, Elsevier, Elsevier, vol. 78(17), pages 2976-2980, December.
  5. 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.
  6. 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, Springer, vol. 66(2), pages 325-344, April.


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