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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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https://doi.org/10.5194/npg-2020-23
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-2020-23
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

  24 Jun 2020

24 Jun 2020

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This preprint is currently under review for the journal NPG.

Application of Lévy Processes in Modelling (Geodetic) Time Series With Mixed Spectra

Jean-Philippe Montillet1,2, Xiaoxing He3, Kegen Yu4, and Changliang Xiong5 Jean-Philippe Montillet et al.
  • 1Physikalisch - Meteorologisches Observatorium Davos / World Radiation Center, Davos, Switzerland
  • 2Space and Earth Geodetic Analysis laboratory (SEGAL), University Beira Interior, Covhila, Portugal
  • 3School of Civil Engineering and Architecture, East China Jiaotong University, Nan Chang, China
  • 4School of Environmental Science and Spatial Informatics, China University of Mining and Technology, Xuzhou, China
  • 5Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Science (CAS), Xiaohongshan West Road, Wuhan, China

Abstract. Recently, various models have been developed, including the fractional Brownian motion (fBm), to analyse the stochastic properties of geodetic time series, together with the estimated geophysical signals. The noise spectrum of these time series is generally modelled as a mixed spectrum, with a sum of white and coloured noise. Here, we are interested in modelling the residual time series, after deterministically subtracting geophysical signals from the observations. This residual time series is then assumed to be a sum of three stochastic processes, including the family of Lévy processes. The introduction of a third stochastic term models the remaining residual signals and other correlated processes. Via simulations and real time series,we identify three classes of Lévy processes: Gaussian, fractional and stable. In the first case, residuals are predominantly constituted of short-memory processes. Fractional Lévy process can be an alternative model to the fBm in the presence of long-term correlations and self-similarity property. Stable process is here restrained to the special case of infinite variance, which can be only satisfied in the case of heavy-tailed distributions in the application to geodetic time series. Therefore, it implies potential anxiety in the functional model selection where missing geophysical information can generate such residual time series.

Jean-Philippe Montillet et al.

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Jean-Philippe Montillet et al.

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Short summary
Recently, various models have been developed, including the fractional Brownian motion (fBm), to analyse the stochastic properties of geodetic time series, together with the estimated geophysical signals. The noise spectrum of these time series is generally modelled as a mixed spectrum, with a sum of white and coloured noise. Here, we are interested in modelling the residual time series, after deterministically subtracting geophysical signals from the observations.
Recently, various models have been developed, including the fractional Brownian motion (fBm),...
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