2021
DOI: 10.5194/npg-28-121-2021
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Application of Lévy processes in modelling (geodetic) time series with mixed spectra

Abstract: 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 ass… Show more

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Cited by 4 publications
(3 citation statements)
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“…Nonetheless, the steepness of this ramp shows the degree of correlation or the type of stochastic noise within the time series, by fitting a power-law model such as S(f) ∼ 1/f β . The exponent β defines the type of colored noise: flicker noise corresponds to β equal to 1, a random walk to β equal to 2, and white noise with β equal to 0 (J.-P. Montillet et al, 2021).…”
Section: 1029/2021jd036146mentioning
confidence: 99%
“…Nonetheless, the steepness of this ramp shows the degree of correlation or the type of stochastic noise within the time series, by fitting a power-law model such as S(f) ∼ 1/f β . The exponent β defines the type of colored noise: flicker noise corresponds to β equal to 1, a random walk to β equal to 2, and white noise with β equal to 0 (J.-P. Montillet et al, 2021).…”
Section: 1029/2021jd036146mentioning
confidence: 99%
“…Nonetheless, the steepness of this ramp shows the degree of correlation or the type of stochastic noise within the time series, by fitting a powerlaw model such as S(f ) ∼ 1/f β . The exponent β defines the type of coloured noise: flicker noise corresponds to β equal to 1, a random walk to β equal to 2, and white noise with β equal to 0 (J.-P. Montillet et al, 2021).…”
Section: Time-frequency Analysis Of the Composite Time Seriesmentioning
confidence: 99%
“…of Total Solar Irradiance (TSI) at Solar Minimum (Minimum) Over the Last 41 Years From TSI Time Series (Mean μ and Standard Deviation σ) Released by Dudok de Wit et al (2017) (C1), by Dewitte and Nevens (2016) (C2) and by Fröhlich (2006) (C3) MONTILLET ET AL. 10.1029/2021JD036146 8 of 19flicker noise corresponds to β equal to 1, a random walk to β equal to 2, and white noise with β equal to 0 (J.-P Montillet et al, 2021)…”
mentioning
confidence: 99%