## 4 Results
The CBP's evidence period is significant at 95% (hollow circles) and at 99% (red circles). Among the peaks significant at 99%, the highest ones signal the characteristic modulating frequencies of the IMFs. IMF\({}_{1}\) exhibits periodicities of 4 months and 6 months; IMF\({}_{2}\) is marked by an annual periodicity, while IMF\({}_{3}\) shows periodicities of about 12 months and 25 months; IMF\({}_{4}\) is marked by periods of 28, 36 and 53 months, while IMF\({}_{5}\) by a cycle of 60 months. IMF\({}_{6}\) and IMF\({}_{7}\) represent the long-term components of the monthly counts, since they are modulated by periods corresponding approximately to the length of the series. Figure 4: Monthly total burned area versus monthly number of fires. Figure 8 shows the results of the EMD of the monthly total area, and Figure 9 shows the CBP of the IMFs. The first two IMFs are characterized by the same modulating frequencies as the first two IMFs in the monthly counts. The third IMF shows only one main characteristic periodicity at 12 months. The fourth IMF is mainly modulated by 26-month and 48-month periodicities, while the fifth one mainly by a 60-month periodicity. IMF\({}_{6}\) and IMF\({}_{7}\) represent the long-term components of the monthly burned area as for the monthly counts. Table 1 shows the main periodicities for each IMF of the monthly number and burned area series (the highest one is in bold). Figure 5: Relationship between (**a**) the Allan Factor (AF) and the windows of duration \(\tau\) and (**b**) the Schuster’s spectrum and the tested period. The AF and Schuster’s spectrum were used to characterize the time dynamics of fires (2004–2023) in the Basilicata region, Southern Italy. The arrows indicate the characteristics timescales and periodicities of the fire sequence. The black and red dotted lines in (**a**) represent the 97.5% confidence curves for Poissonian and random shuffles, respectively. Figure 6: Residual and Intrinsic Mode Functions (IMFs) after applying Empirical Mode Decomposition (EMD) to the monthly number of fires (2004–2023) in the Basilicata region, Southern Italy. Figure 8: Residual and Intrinsic Mode Functions (IMF1-IMF7) after applying Empirical Mode Decomposition (EMD) to the monthly total burned area (2004–2023) in the Basilicata region, Southern Italy. Figure 7: Correlogram-based periodogram (CBP) of the Intrinsic Mode Functions (IMFs) for the monthly number of fires in the Basilicata region, Southern Italy. The plots from (**top**) to (**bottom**) correspond to the Intrinsic Mode Functions (IMF1 to IMF7), respectively. The periods significant at the 0.01 level are marked by filled red circles; those significant at 0.05, by hollow circles. The monthly counts and the monthly total burned area unveil various components: intra-annual, with the main modulating periods at 4 and 6 months; annual; quasi-bi-annual; intermediate-term, with the main modulating periods from about 3 to 5 years; and long-term, with the main modulating periods at about 20 years. We explored the relationship between SPEI\({}_{B}\) (calculated for the Basilicata region) and the IMF components of monthly counts and total burned area derived from EMD. Pearson's correlation coefficient \(\rho\) was computed between each SPEI\({}_{B}(T_{a})\) for \(T_{a}=1,\ldots,48\) and each IMF. The left panels of Figures 10 and 11 illustrate the correlation coefficient \(\rho\) as a function of \(T_{a}\) for the monthly counts and monthly total burned area, respectively. At the top of each plot in the left panel, the maximum \(|\rho|\), its \(p\)-value, and the corresponding accumulation time \(T_{a,max}\) are displayed. The right panels of Figures 10 and 11 exhibit the comparison between the SPEI\({}_{B}\) at \(T_{a,max}\) alongside the corresponding IMF. Taking into