Autoregressive Wild Bootstrap Inference for Nonparametric Trends

Marina Friedrich, Stephan Smeekes, Jean-Pierre Urbain

Research output: Working paper / PreprintWorking paper

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In this paper a modified wild bootstrap method is presented to construct pointwise confidence intervals around a nonparametric deterministic trend model. We derive the asymptotic distribution of a nonparametric kernel estimator of the trend function under general conditions, which allow for serial correlation and heteroskedasticity. Asymptotic validity of the bootstrap method is established and it is shown to work well in finite samples in an extensive simulation study. The bootstrap method has the potential of providing simultaneous confidence bands for the same models along the lines of Bühlmann (1998) and can be applied without further adjustments to missing data. We illustrate this by applying the proposed method to a time series of atmospheric ethane which can be used as an indicator of atmospheric pollution and transport.
Original languageEnglish
PublisherMaastricht University, Graduate School of Business and Economics
Publication statusPublished - 1 May 2017

Publication series

SeriesGSBE Research Memoranda

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

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