# Forecasting Cost Risks of Corn and Soybean Crops through Monte Carlo Simulation
## 2 Materials and Methods
### Time Series Forecasting Based on Historical Data
Figure 7A,B presents the trends  
Figure 5: Price trend for the next 24 months of the fungicide variable Trifloxystrobin Tebuconazole (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). Figure 6: Price trend for the next 24 months of the variable soybean seed (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). for these variables, respectively. Both variables indicate an upward trend for the next 24 months. The minimum cost per hectare for corn/soybean, as shown in Figure 7A, was USD 2.52, and, for Figure 7B, was USD 3.31. The average costs were USD 2.83 and USD 3.84, and the maximum costs were USD 3.23 and USD 4.72, with standard deviations of USD 0.22 and USD 0.42, respectively. The forecasted average values are aligned with the current values of USD 2.83 for tractor drivers and USD 3.84 for day workers [29]. The ARIMA models for Figure 7A,B demonstrated that the series has an insignificant autoregressive (AR) component. This is evident from the partial autocorrelations of the series, as shown in the ARIMA (0, 2, 0) model. The values of the DW statistic indicate that there is no first-order correlation, either positive or negative, with a value of 2.0 for Figure 7A and close to 2.0 for Figure 7B. The results presented in Figure 8 are related to the price trend per corn bushel soon. However, it is evident that there is a stable price trend for corn per bushel in the coming 24 months. The minimum price per bag for corn, as shown in Figure 8, was USD 5.66. The average price was USD 11.28, and the maximum price was USD 18.53, with a standard deviation of USD 4.52. The current price is USD 11.3, which falls within the predicted price range of this analysis (IEA, 2023). Using the penalizing criteria of AIC and BIC, like Figure 3A, the ARIMA (1, 1, 1) model was found to be the best fit for the series. The AIC value was \(-\)0.65, and the BIC value was \(-\)5.58 *, based on the lowest mean squared error. The statistical values for the MCS analysis conducted using the predictor, presented in the Figures 3-8 (through a normal distribution), are summarized in Table 4.  
Figure 8: Price trend for the next 24 months of corn per bag (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). Figure 7: Price trend for the next 24 months of the tractor driver labor costs (**A**) and day workers labor costs (**B**) (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). Thus, the results showed that inputs such as the NPK 05-25-25 fertilizer, Urea fertilizer, Dolomitic Limestone corrective, Triflozystrobin Tebuconazole fungicide, soybean seed, day workers, tractor hours, and corn seed are relevant variables in estimating the production costs of corn and soybeans. Furthermore, cost forecasting using a Monte Carlo simulation provided a clear view of the expected costs for the next 24 months, enabling farmers to make strategic planning and resource allocation decisions. The results also suggest a reduction in fertilizer costs, an increase in labor costs, soybean seed and fungicide costs, and stability in dolomitic limestone corrective costs in the near future (24 months). From the Monte Carlo simulation (MCS), the range of corn production costs is between USD 600.00 and USD 1150.00, with a level of certainty of 84.7%; and, of soybean production, costs between USD 260.00 and USD 420.00, with a level of certainty of 86.4%. These ranges of values demonstrate a high-cost risk level. Our findings also revealed that soybean profitability is higher than corn profitability based on the variables analyzed in this study.