Nonparametric estimation and bootstrap inference on trends in atmospheric time series: an application to ethane

Marina Friedrich, Eric Beutner, Hanno Reuvers, Stephan Smeekes, Jean-Pierre Urbain, Whitney Bader, Bruno Franco, Bernard Lejeune, Emmanuel Mahieu

Research output: Working paperProfessional

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Abstract

Understanding the development of trends and identifying trend reversals in decadal time series is becoming more and more important. Many climatological and atmospheric time series are characterized by autocorrelation, heteroskedasticity and seasonal effects. Additionally, missing observations due to instrument failure or unfavorable measurement conditions are common in such series. This is why it is crucial to apply methods which work reliably under these circumstances. The goal of this paper is to provide a toolbox which can be used to determine the presence and form of changes in trend functions using parametric as well as nonparametric techniques. We consider bootstrap inference on broken linear trends and smoothly varying nonlinear trends. In particular, for the broken trend model, we propose a bootstrap method for inference on the break location and the corresponding changes in slope. For the smooth trend model we construct simultaneous confidence bands around the nonparametrically estimated trend. Our autoregressive wild bootstrap approach combined with a seasonal filter, is able to handle all issues mentioned above. We apply our methods to a set of atmospheric ethane series with a focus on the measurements obtained above the Jungfraujoch in the Swiss Alps. Ethane is the most abundant non-methane hydrocarbon in the Earth's atmosphere, an important precursor of tropospheric ozone and a good indicator of oil and gas production as well as transport. Its monitoring is therefore crucial for the characterization of air quality and of the transport of tropospheric pollution.
Original languageEnglish
PublisherarXiv.org at Cornell University Library
Publication statusPublished - 13 Mar 2019

Keywords

  • stat.AP
  • econ.EM

Cite this

Friedrich, M., Beutner, E., Reuvers, H., Smeekes, S., Urbain, J-P., Bader, W., ... Mahieu, E. (2019). Nonparametric estimation and bootstrap inference on trends in atmospheric time series: an application to ethane. arXiv.org at Cornell University Library.
Friedrich, Marina ; Beutner, Eric ; Reuvers, Hanno ; Smeekes, Stephan ; Urbain, Jean-Pierre ; Bader, Whitney ; Franco, Bruno ; Lejeune, Bernard ; Mahieu, Emmanuel. / Nonparametric estimation and bootstrap inference on trends in atmospheric time series: an application to ethane. arXiv.org at Cornell University Library, 2019.
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abstract = "Understanding the development of trends and identifying trend reversals in decadal time series is becoming more and more important. Many climatological and atmospheric time series are characterized by autocorrelation, heteroskedasticity and seasonal effects. Additionally, missing observations due to instrument failure or unfavorable measurement conditions are common in such series. This is why it is crucial to apply methods which work reliably under these circumstances. The goal of this paper is to provide a toolbox which can be used to determine the presence and form of changes in trend functions using parametric as well as nonparametric techniques. We consider bootstrap inference on broken linear trends and smoothly varying nonlinear trends. In particular, for the broken trend model, we propose a bootstrap method for inference on the break location and the corresponding changes in slope. For the smooth trend model we construct simultaneous confidence bands around the nonparametrically estimated trend. Our autoregressive wild bootstrap approach combined with a seasonal filter, is able to handle all issues mentioned above. We apply our methods to a set of atmospheric ethane series with a focus on the measurements obtained above the Jungfraujoch in the Swiss Alps. Ethane is the most abundant non-methane hydrocarbon in the Earth's atmosphere, an important precursor of tropospheric ozone and a good indicator of oil and gas production as well as transport. Its monitoring is therefore crucial for the characterization of air quality and of the transport of tropospheric pollution.",
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Friedrich, M, Beutner, E, Reuvers, H, Smeekes, S, Urbain, J-P, Bader, W, Franco, B, Lejeune, B & Mahieu, E 2019 'Nonparametric estimation and bootstrap inference on trends in atmospheric time series: an application to ethane' arXiv.org at Cornell University Library.

Nonparametric estimation and bootstrap inference on trends in atmospheric time series: an application to ethane. / Friedrich, Marina; Beutner, Eric; Reuvers, Hanno; Smeekes, Stephan; Urbain, Jean-Pierre; Bader, Whitney; Franco, Bruno; Lejeune, Bernard; Mahieu, Emmanuel.

arXiv.org at Cornell University Library, 2019.

Research output: Working paperProfessional

TY - UNPB

T1 - Nonparametric estimation and bootstrap inference on trends in atmospheric time series: an application to ethane

AU - Friedrich, Marina

AU - Beutner, Eric

AU - Reuvers, Hanno

AU - Smeekes, Stephan

AU - Urbain, Jean-Pierre

AU - Bader, Whitney

AU - Franco, Bruno

AU - Lejeune, Bernard

AU - Mahieu, Emmanuel

PY - 2019/3/13

Y1 - 2019/3/13

N2 - Understanding the development of trends and identifying trend reversals in decadal time series is becoming more and more important. Many climatological and atmospheric time series are characterized by autocorrelation, heteroskedasticity and seasonal effects. Additionally, missing observations due to instrument failure or unfavorable measurement conditions are common in such series. This is why it is crucial to apply methods which work reliably under these circumstances. The goal of this paper is to provide a toolbox which can be used to determine the presence and form of changes in trend functions using parametric as well as nonparametric techniques. We consider bootstrap inference on broken linear trends and smoothly varying nonlinear trends. In particular, for the broken trend model, we propose a bootstrap method for inference on the break location and the corresponding changes in slope. For the smooth trend model we construct simultaneous confidence bands around the nonparametrically estimated trend. Our autoregressive wild bootstrap approach combined with a seasonal filter, is able to handle all issues mentioned above. We apply our methods to a set of atmospheric ethane series with a focus on the measurements obtained above the Jungfraujoch in the Swiss Alps. Ethane is the most abundant non-methane hydrocarbon in the Earth's atmosphere, an important precursor of tropospheric ozone and a good indicator of oil and gas production as well as transport. Its monitoring is therefore crucial for the characterization of air quality and of the transport of tropospheric pollution.

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Friedrich M, Beutner E, Reuvers H, Smeekes S, Urbain J-P, Bader W et al. Nonparametric estimation and bootstrap inference on trends in atmospheric time series: an application to ethane. arXiv.org at Cornell University Library. 2019 Mar 13.