## 4 Results  
We analyzed the sequence of fires that occurred in the Basilicata region (Southern Italy) from 2004 to 2023 (Figure 3a). Considering the series of the interevent times (Figure 3b), we found \(C_{\text{p}}=3.96\). To calculate the 95% confidence interval of this estimate, a total of 1000 Poisson surrogate fire sequences were generated, each having the same number of fires and the same mean nterevent time as the original series. The resulting 95% confidence interval for \(C_{v}\) is given by [0.96, 1.03], where the lower and upper bounds correspond to the 2.5 th and 97.5 th percentiles, respectively, of the \(C_{v}\) distribution obtained from the Poissonian surrogate sequences. As can be seen, the fire series is highly time-clusterized at a global scale, being \(C_{v}\) well beyond the 95% confidence interval. The time clustering of the fire sequence is rather high due to the temporal occurrence pattern of fire events, which is much denser during the summer months; therefore, considering the entire sequence, there is an increase in frequency during the summer, structuring the entire sequence as composed of a set of clusters. Figure 3c,d display the monthly number of fires and the monthly total burned area, respectively; the two variables are very similar, as confirmed by the relationship between them (Figure 4). Figure 5a shows the AF for the analyzed fire sequence and the 97.5% confidence level calculated for 100 random sequences obtained with the Poissonian surrogate method and the random permutating method. The confidence envelopes were constructed from the pointwise 97.5 th percentiles of the surrogate ensemble. No additional smoothing was applied to the confidence bands, in order to preserve their natural variability and accurately reflect the statistical variability across timescales. The AF of the original sequence of fires increases with \(\tau\), indicating that the sequence is clusterized in time. The AF is well above the confidence curve obtained by Poissonian surrogates, suggesting that its non-Poissonian character is significant for all the investigated timescales. The AF falls below the confidence level for the random shuffles of interevent times up to approximately one week; this suggests that the clustering behavior is influenced by the probability density of interevent times within this shorter timescale range. Conversely, for longer timescales, the clustering  
Figure 3: Characteristics of the fire time series (2004–2023) in the Basilicata region, Southern Italy: (**a**) burned area; (**b**) interevent time; (**c**) monthly number of fires; and (**d**) monthly burned area (m\({}^{2}\)). behavior depends on the ordering of interevent times. At the 1-year timescale, the AF exhibits a drop, indicating the presence of annual periodic fluctuations in the fire sequence. Between about 2 weeks and 3 months, we can identify a fractal behavior, revealed by the power-law increase of the AF with \(\tau\); within this timescale range the fractal exponent \(\alpha\sim 1.4\), which indicates that the fire series is characterized by correlation among the events. Figure 5b displays the Schuster spectrum. For each tested period, ranging from 1 day up to half the total duration of the observation period, the corresponding \(p\)-value (represented by circles) was computed. Several periods exhibit \(p\)-values below the 99% confidence threshold (indicated by the red line). Notably, periods of approximately 3 months and 1 year stand out as having the lowest \(p\)-values, indicating a strong periodic component at these timescales. The yearly period is in agreement with the annual timescale identified in the previous AF analysis, signaling the presence of the 1-year periodicity in the time dynamics of the fires. In addition, a period of about 5 years is revealed in [PERSON]'s spectrum. We applied the EMD analysis to the monthly number of fires and the monthly total burned area. Figure 6 shows results of the EMD of the monthly counts, while Figure 7 shows the correlogram-based periodogram (CBP) of the IMFs.