# Forecasting Cost Risks of Corn and Soybean Crops through Monte Carlo Simulation
## 2 Materials and Methods
### Time Series Forecasting Based on Historical Data
In other words, a non-stationary stochastic process is one where the joint distribution of any set of variables changes if we change the variables over time. This is due to the partial correlations of the series, as evidenced by the ARIMA (1, 1, 2) model. Additionally, it can be observed from the Durbin-Watson (DW) statistic values that there is a first-order correlation, whether positive or negative, with values close to 2.0, as presented in Figure 3B. The results presented in Figure 4 show the predicted values for dolomitic limestone corrective. The forecast indicates a stable scenario for the predicted 24 months. The minimum cost/ha/soybean/corn value was USD 14.80. The average value was equal to USD 25.29, and the maximum value reached USD 40.98, with a standard deviation of USD 8.02. The current cost of dolomitic limestone corrective per hectare was USD 25.3 [29], which falls within the predicted average. The literature indicates that the costs associated with this soil corrective are mainly influenced by the freight rates during its transportation [67]. According to the Predictor, the best method with the lowest mean squared error chosen for all groups was the Damped Trend Non-Seasonal. Furthermore, it can be observed that the values of the Durbin-Watson statistic indicate no first-, second-, or third-order correlations, whether positive or negative. The analyzed material is essential for the cultivation of corn/soybean, as soil acidification is a concern in almost all countries with significant production of these crops, and its reversal contributes to water and nutrient exploitation, aiding the plant during periods of drought [68]. The results presented in Figure 5 show the estimated values of the Fungicide Trifloxystrobin Tebuconazole, which showed a strong relationship with the production costs of  
Figure 4: Price trend for the next 24 months of the dolomitic limestone corrective (green line: historical data, blue line: fitted and forecast; orange area: forecast range with lower and upper bounds of 2.5% and 97.5%, respectively). corn and soybean. The forecast indicates a scenario of price increase for the subsequent 24 months. This fungicide was the only agricultural pesticide with R\({}^{2}\geq\) 0.70 for both crops and, thus, it can influence the increase in production costs for the studied crops. The minimum cost per hectare for soybean/corn, as shown in Figure 5, was USD 25.43. The average cost was USD 28.92, and the maximum cost was USD 33.99, with a standard deviation of USD 2.64. According to [29], the cost at that moment of Trifloxystrobin Tebuconazole per hectare was USD 28.9, indicating that although there is a trend of price increase for this input over the next 24 months, the average cost remained within the estimated price by this forecast. The statistical results conducted, according to the Predictor, showed that the best method with the lowest mean squared error chosen for all groups was DTN-S. This method is efficient for data with trends but without seasonality [32], which was the case in this analysis. The estimated values for soybean seeds are presented in Figure 6. The results correspond to the values for both analyzed crops as dependent variables (corn/soybean). The forecast indicates a scenario of price increase for the next two years. The minimum cost per hectare for soybean seed was USD 34.29. The average cost was USD 79.93, and the maximum cost was USD 137.14, with a standard deviation of USD 33.28. The cost of soybean seed per hectare was USD 79.9 [53]. This value also falls within the predicted average produced by our model. For the variable soybean seed, the most suitable method was DES. The results showed that the values of the DW statistic among all groups are close to 2.0. Figure 7, presented below, shows the values and trends for the costs related to tractor drivers and day workers for both crops (corn/soybean).