# Forecasting Cost Risks of Corn and Soybean Crops through Monte Carlo Simulation
## 2 Materials and Methods
### Monte Carlo Simulation
#### 2.5.2 Autoregressive Integrated Moving Average (ARIMA)
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline  & **DOIL** & **FUTT** & **HEGL** & **INTL** & **DLLC** & **NPKF** & **DLR** & **SOY** & **COR** & **SOYS** & **CORS** & **TRAC** & **DAI** & **PCF** & **URF** \\ \hline n & 60 & 60 & 60 & 60 & 60 & 60 & 60 & 60 & 60 & 60 & 60 & 60 & 60 & 60 & 60 \\ MIN & 0.57 & 16.95 & 18.91 & 29.59 & 14.8 & 278.4 & 3.18 & 12.61 & 5.66 & 0.57 & 2.33 & 302.26 & 13.25 & 352.38 & 339.04 \\ MAX & 1.41 & 22.66 & 92.02 & 48.68 & 4.09 & 1205.24 & 5.67 & 36.51 & 18.53 & 2.29 & 4.31 & 387.01 & 18.9 & 1256.62 & 1201.48 \\ RANGE & 0.84 & 5.71 & 73.11 & 19.09 & 26.18 & 296.84 & 2.49 & 23.9 & 12.87 & 1.72 & 1.98 & 84.75 & 5.65 & 904.25 & 862.43 \\ MEAN & 0.80 & 19.28 & 36.22 & 38.17 & 25.28 & 576.03 & 4.66 & 22.57 & 11.27 & 1.332 & 3.299 & 2.83 & 15.57 & 602.53 & 580.38 \\ VAR & 0.0586 & 3.1021 & 625.35 & 24.85 & 64.30 & 140.43 & 5.986 & 72.13 & 20.39 & 3.076 & 0.114 & 70.68 & 2.81 & 1133.071 & 895.98 \\ SD & 0.24 & 1.7613 & 25.007 & 4.9851 & 80.0191 & 323.16 & 0.77 & 8.4991 & 4.5157 & 0.55 & 0.33 & 26.58 & 1.67 & 336.61 & 293.18 \\ CV & 30.15 & 9.1\% & 69.0\% & 13.1\% & 31.7\% & 56.1\% & 16.6\% & 37.6\% & 40.0\% & 41.6\% & 10.2\% & 7.88 & 10.9\% & 55.8\% & 50.5\% \\ SKEW (g1) & 1.2158 & 0.8324 & 1.3291 & 0.3488 & 0.73 & 0.947 & \(-\)0.265 & 0.2153 & 0.2287 & 0.4712 & \(-\)0.2119 & 0.2249 & 6.628 & 10.455 & 1.0692 \\ KUET (g2) & 0.0765 & \(-\)1.2366 & 0.206 & \(-\)0.7111 & \(-\)0.7956 & \(-\)0.8431 & \(-\)1.443 & \(-\)1.7728 & 1.693 & \(-\)1.4971 & 1.1549 & \(-\)1.2933 & \(-\)0.6398 & \(-\)0.7136 & \(-\)0.5489 \\ \hline \end{tabular}  
* n: sample size (monthly data collected from 2018 to 2022); MIN: minimum; MAX: maximum; RANGE: total range; MEAN: arithmetic mean; VAR: variance; SD: standard deviation; CV: coefficient of variation; SKEW: skewness; KURT: kurtosis; DOLL: diesel oil (L); FUTT: fungicide trifloxystrobin tebuconazole[L]; HEGL: herbicide glyphosate (L); INTL: insecticide thiamethoxam lambda-cyhalothrin (L); DLLC: dolomitic limestone corrective (ton); NPKF: NPK 05-25-25 fertilizer (ton); DLR: dollar exchange rate; SOY: soybean bag (kg); COR: corn bag (kg); SOYS: soybean seed (kg); CORS: corn seed (kg); TRAC: tractor driver hours (h); DAI: daily worker hours (h); PCF: potassium chloride fertilizer (kg); URF: urea fertilizer (kg).  
\end{table} 
Table 1: Descriptive measures referring to variables related to the cost of production of corn and soybeans (USD) from January 2018 to December 2022.  
negative skewness distributions, meaning that they remained below the average for a significant part of the analyzed period. Despite reaching high values at times, the dollar remained below the average in recent years due to a combination of factors, including a decline in the performance of the US economy, which has not remained as strong due to global instabilities and political tensions [44]. Regarding corn seed, its price in Sao Paulo is influenced by the price in Sorriso-MT and in Paraguay, as they are, respectively, the main national production areas and the origin of most of the corn imported by Brazil [45]. For the analysis of kurtosis, it was evident that the prices of corn seed exhibited a platykurtic distribution, meaning that the values were more concentrated around the mean. The price of corn seed in Sao Paulo increased by 120% from 2018 (USD 1827.1) to 2022 (USD 4028.54). This significant variability can be explained by changes in the commodities market and currency fluctuations that affect corn costs [46; 47; 48]. Regarding the price of the herbicide glyphosate and the price of diesel fuel, the mesokurtic distribution found for these inputs (moderate concentration of values around the mean) may be related to economic and environmental factors related to the production, supply, and demand of these products [49; 41]. The remaining variables exhibited a leptokurtic distribution (relatively low concentration of values around the mean).