## 2 Materials and Methods
### Singular Spectrum Analysis and Index Insurance  
We used the _first_ component result from the PCA to obtain its signal using an SSA methodology. With the signal extracted, we calculate the payouts (POs). Next, we determined the expected payments exclusively caused by the tendency components for the next two years (Figure 9). These disbursements represent payments in excess or additional to those that belonged to seasonal patterns. Unlike in dry months, during wet months, an increasing disbursal due to tendency components is expected. We estimated the average POERs (calculated as future POs for tendency and the maximum indemnity, MI amount) (Table 7) for a common coffee crop producer near each weather station. This was reported in the first component (Table 3) in concordance with each crop season. For instance, during the wet months, it is expected that POs increase to 19% and 60% in the first and second years, respectively, with respect to regular seasonal disbursals (Figure 9). This could be interpreted as extra payments because of the effect of extreme rain conditions. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Season** & **n** & **Mean** & **sd** & **Median** & **Min** & **Max** & **Skew** & **Kurtosis** & **se** \\ \hline Wet & 1378 & 293.69 & 232.6 & 267.06 & 0 & 1551.74 & 0.91 & 1 & 6.27 \\ Dry & 846 & 201.95 & 209.05 & 145.69 & 0 & 1995.92 & 2.42 & 11.16 & 7.19 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Summary statistics for dry and wet seasons in the 1 st component. Source: author’s processing. Figure 8: Kernel pdfs with n = 1000 points, results for 1 st component in the (**a**) wet season and (**b**) dry season of monthly average rainfall values (2010–2019). Source: author’s processing. We applied a tendency significance test, specifically, the Mann-Kendall test, to the reconstructed tendency series (Appendix A, Table A1). The results show that both seasonal tendencies are significant at 95% confidence. These significant effects can also be identified in the SSA results, where the singular eigenvectors show that the tendency component accounts for most of the variation in the series with 79% and 94% for wet and dry seasons, respectively. In terms of coffee crop quality, the shapes of the density distributions and the summary statistics (Figure 8, Table 6) indicate that the current and future quality of the crops in the regions of the first component could be at risk. It is at risk as the transition from the flowering to the filling phase usually occurs in the stages of the dry season, and this requires stable irrigation levels that are not happening [55]. This effect can be seen in Figure 9, which depicts the tendency of the dry season. In Colombia, there are currently coffee index insurance programs that have had positive results. One positive example is Cafe Seguro [33]. Besides the use of weather stations and satellite data these programs use, the reason for their success may be that they promote a closed approach to farmers and cooperatives to narrow gaps regarding their challenges and the needs of the agricultural insurance programs. These programs \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Season**} & \multicolumn{3}{c}{**Payout Exceedance PoE**} & \multicolumn{2}{c}{**PoE Ratio (\%)**} \\ \cline{2-5}  & **Year 1 (SCOP/Month*ha)** & **Year 2 (SCOP/Month*ha)** & **Year 1** & **Year 2** & **POERs Forecast** \\  & & & & **Tendency Direction** \\ \hline Wet & 491,528.90 & 1,568,978 & 18.56 & 59.27 & \(\uparrow\) \\ Dry & 695,868.10 & 582,540.40 & 26.28 & 22 & \(\downarrow\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Future payouts in exceedance (PoEs) and ratios (POERs) for 2 years ahead. Note: arrows reflect the direction of the tendency. Source: author’s processing. Figure 9: Decomposition of POs for seasonality and tendency in wet and dry months. Source: author’s processing. could be an example to learn from and to promote insurance use by coffee farmers in more productive regions.