  The aim of this research is to identify an efficient model to describe the
fluctuations around the trend of the soil temperatures monitored in the
volcanic caldera of the Campi Flegrei area in Naples (Italy). The study focuses
on the data concerning the temperatures in the mentioned area through a
seven-year period. The research is initially finalized to identify the
deterministic component of the model, given by the seasonal trend of the
temperatures, which is obtained through an adapted regression method on the
time series. Subsequently, the stochastic component from the time series is
tested to represent a fractional Brownian motion (fBm). An estimation based on
the periodogram of the data is used to estabilish that the data series follows
a fBm motion, rather then a fractional Gaussian noise. An estimation of the
Hurst exponent $H$ of the process is also obtained. Finally, an inference test
based on the detrended moving average of the data is adopted in order to assess
the hypothesis that the time series follows a suitably estimated fBm.
