Autoregressive Wild Bootstrap Inference for Nonparametric Trends

Marina Friedrich, Stephan Smeekes, Jean-Pierre Urbain

Research output: Working paperProfessional

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In this paper we propose an autoregressive wild bootstrap method to construct confidence bands around a smooth deterministic trend. The bootstrap method is easy to implement and does not require any adjustments in the presence of missing data, which makes it particularly suitable for climatological applications. We establish the asymptotic validity of the bootstrap method for both pointwise and simultaneous confidence bands under general conditions, allowing for general patterns of missing data, serial dependence and heteroskedasticity. The finite sample properties of the method are studied in a simulation study. We use the method to study the evolution of trends in daily measurements of atmospheric ethane obtained from a weather station in the Swiss Alps, where the method can easily deal with the many missing observations due to adverse weather conditions.
Original languageEnglish
Publication statusPublished - 6 Jul 2018

Publication series

SeriesarXiv e-prints

JEL classifications

  • c14 - Semiparametric and Nonparametric Methods: General
  • c22 - "Single Equation Models; Single Variables: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models"


  • autoregressive wild bootstrap
  • nonparametric estimation
  • time series
  • simultaneous confidence bands
  • trend estimation

Research Output

  • 1 Working paper

Autoregressive Wild Bootstrap Inference for Nonparametric Trends

Friedrich, M., Smeekes, S. & Urbain, J-P., 1 May 2017, Maastricht University, Graduate School of Business and Economics, (GSBE Research Memoranda; No. 010).

Research output: Working paperProfessional

Open Access
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Cite this

Friedrich, M., Smeekes, S., & Urbain, J-P. (2018). Autoregressive Wild Bootstrap Inference for Nonparametric Trends. arXiv e-prints, No. 1807.02357