  Recently, various models have been developed, including the fractional
Brownian motion (fBm), to analyse the stochastic properties of geodetic time
series, together with the extraction of geophysical signals. The noise spectrum
of these time series is generally modeled 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
random variables (r.v.), with the last r.v. belonging to the family of Levy
processes. This stochastic term models the remaining residual signals and other
correlated processes. Via simulations and real time series, we identify three
classes of Levy processes: Gaussian, fractional and stable. In the first case,
residuals are predominantly constituted of short-memory processes. Fractional
Levy process can be an alternative model to the fBm in the presence of
long-term correlations and self-similarity property. Stable process is
characterized by a large variance, which can be satisfied in the case of
heavy-tailed distributions. The application to geodetic time series imply
potential anxiety in the functional model selection where missing geophysical
information can generate such residual time series.
