On the analysis of the temperature fluctuation in the Campi Flegrei caldera through a fractional Brownian motion-based model

The aim of this research is to identify a model able to describe the fluctuations 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 (cf. Sabbarese et al. [14]). The deterministic component of the model, given by the seasonal trend of the temperatures, is obtained through a regression method on the time series. A fractional Brownian motion (fBm) is chosen to represent the residual process between the seasonal trend and the time series. This is validated through a suitable test and an estimation based on the periodogram of the data. Thereafter, the Hurst exponent of the process is estimated by means of a method proposed by Cannon et al. [2]. Finally, an inference test based on the detrended moving average of the data is adopted in order to confirm that the residual series follows a fBm.