Autoregressive Wild Bootstrap Inference for Nonparametric Trends

Marina Friedrich, Stephan Smeekes, Jean-Pierre Urbain

Research output: Working paperProfessional

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Abstract

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

Keywords

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

Cite this

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title = "Autoregressive Wild Bootstrap Inference for Nonparametric Trends",
abstract = "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.",
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Autoregressive Wild Bootstrap Inference for Nonparametric Trends. / Friedrich, Marina; Smeekes, Stephan; Urbain, Jean-Pierre.

2018.

Research output: Working paperProfessional

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T1 - Autoregressive Wild Bootstrap Inference for Nonparametric Trends

AU - Friedrich, Marina

AU - Smeekes, Stephan

AU - Urbain, Jean-Pierre

N1 - Data Source: Network for the Detection of Atmospheric Composition Change, ftp://ftp.cpc.ncep.noaa.gov/ndacc/station/jungfrau/hdf/ftir/

PY - 2018/7/6

Y1 - 2018/7/6

N2 - 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.

AB - 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.

KW - autoregressive wild bootstrap

KW - nonparametric estimation

KW - time series

KW - simultaneous confidence bands

KW - trend estimation

M3 - Working paper

BT - Autoregressive Wild Bootstrap Inference for Nonparametric Trends

ER -