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.

翻译：这项研究的目的是确定一个模型,能够描述那不勒斯(意大利)坎皮弗列格里地区火山口中监测的土壤温度波动情况,研究的重点是关于七年期间上述地区温度的数据(见Sabbarese等人,[14]),模型的决定因素部分,根据温度的季节趋势,通过时间序列的回归法获得,选择了分数布朗运动(fBm)代表季节趋势与时间序列之间的剩余过程,通过适当的测试和根据数据周期图进行的估计加以验证。随后,过程的赫斯特亮度通过Cannon等人建议的方法加以估计。 [2]最后,根据数据分流平均移动法进行的推断试验,以证实剩余序列遵循FBm。