Soybean Export Through the Port of Santos: Predictive Modeling with Time Series and Exogenous Variables

Daniele Siqueira; Aimée Shirozono

DOI: 10.22167/2675-6528-202602817

Article derived from a Final Course Work (TCC), with content based on the student’s original work and adapted to the editorial format of the E&S Magazine with the support of the ResumeAI tool, an artificial intelligence solution developed by Instituto Pecege for textual synthesis and organization.

Summary

The growth of Brazilian soybean exports and the central role of the port of Santos as the main channel for grain outflow have highlighted, in recent years, the importance of tools to aid logistical planning and minimize economic losses. The objective was to develop a predictive model for monthly soybean shipments through the São Paulo port, focusing on the first semester of the year, a period when exports are concentrated. For this purpose, a monthly time series of shipments between January 2010 and December 2024 was used. The SARIMA model was applied after exploratory data analysis. Subsequently, to improve the predictive fit, two exogenous variables were selected for the SARIMAX model: one related to the availability of soybeans in the main producing states that ship through Santos, constructed via Principal Component Analysis (PCA), and another as an approximation of the port’s operational performance. The SARIMA model showed better predictive performance compared to the five combinations tested in the SARIMAX model, as the exogenous variables did not consistently contribute to improving the forecasts. The need to include more representative exogenous variables of the monthly soybean export dynamics for future model improvements was identified.

Keywords: Agribusiness; Foreign trade; Port logistics; PCA; SARIMAX.

1. Introduction

Brazil stands out as the world’s largest producer and exporter of soybeans in grain, a position consolidated from the 2012/13 and 2019/20 harvests, when it surpassed the United States. In the 2023/24 harvest, the country was responsible for 59% of global soybean exports and 39% of global production, according to data from the U.S. Department of Agriculture (USDA, 2025). This prominence gives soybeans a central role in the Brazilian economy, with the production chain (grain, meal, and oil) and biodiesel contributing 27% of agribusiness GDP and 7% of national GDP in 2022, totaling R$ 674 billion (CEPEA & ABIOVE, 2023). Brazilian soybean production grew 721% between 1991 and 2022, from 15.4 million to 126.5 million tons (CONAB, 2025), driven, in part, by the growing demand from China, which in 2024 accounted for 73% of Brazilian soybean exports (MDIC, 2025a).

Brazil’s consolidation as a global leader in soybean exports is intrinsically linked to the growth of the port of Santos, in São Paulo. Since 2004, the port has become the main channel for grain outflow, exporting 28 million tons in 2024, a fivefold increase compared to twenty years prior (MDIC, 2025a). As the largest port in Latin America, Santos has historically been responsible for at least 25% of all Brazilian foreign trade (APS, 2025b). This concentration of operations generates intense competition for space and time among the various products shipped and un-shipped. The majority of the soybean volume exported by Santos, approximately 70% between 2004 and 2024, originates from Mato Grosso and Goiás (MDIC, 2025a), distant producing states with harvests and shipments concentrated in the first semester.

Given this scenario, the predictability of the soybean export flow becomes crucial for economic agents. Storage and transportation difficulties between harvest and shipment on ships result in the loss of comparative advantages of Brazilian production (Salin, 2025). Adequate export flow forecasts and efficient logistical planning are essential to minimize economic losses (Fiskin et al., 2022). However, the complexity of agricultural product shipments, such as soybeans, is influenced by external shocks, including climatic factors, crop failures, and logistical bottlenecks.

Studies on export volumes frequently employ univariate time series, which consider only historical port traffic data (Lee & Bang, 2024). This approach, however, is insufficient to capture the complex dynamics of soybean exports, which require the incorporation of exogenous and seasonal variables. The need to improve the predictive capacity of these models, considering external factors that directly impact shipping volumes, justifies the search for more robust approaches.

The development of predictive tools that consider this complexity is, therefore, fundamental to optimizing planning and decision-making in the agricultural sector. This study is justified by the need to improve the accuracy of soybean export forecasts, contributing to more efficient logistics management and loss minimization. The objective of this work was to develop a predictive model for monthly soybean shipments through the port of Santos, to be used as an auxiliary tool for planning and decision-making in an agricultural market consultancy. The model was built for the prediction of shipments in the first semester, a period when soybean exports through the São Paulo port are concentrated.

2. Material and Methods

This work was characterized as a research of an applied, empirical, and observational nature, with a quantitative methodological approach. The study aimed to develop a predictive model for the monthly soybean shipments made by the port of Santos, in São Paulo. The tool aimed to assist in planning and decision-making in an agricultural market consultancy, focusing on predicting shipments for the first semester.

The unit of analysis consisted of a monthly time series of soybean exports through the port of Santos, defined as the response variable. The data were collected from the Foreign Trade Statistics System of the Ministry of Development, Industry, Trade and Services (MDIC, 2025a). The series covered the period from January 2010 to December 2024, totaling 180 observations. The choice of this period was determined by the availability of data for the exogenous variables.

In preparing the response variable, the original data in kilograms were converted to millions of tons. Observations with a zero value, indicating months with no shipments, were replaced by a minimum value (0.000000089 million tons). This adjustment allowed for the application of logarithmic transformations and the multiplicative seasonal decomposition of the series, procedures fundamental to time series analysis.

The first exogenous variable, “Factor 1 – Soybean availability in Mato Grosso, Goiás, and São Paulo”, was constructed to approximate the monthly availability of the grain in the main producing states that ship through Santos. Its composition derived from four data series for MT, GO, and SP: initial soybean stocks (IBGE, 2025), soybean production (CONAB, 2025), harvested percentage of the ongoing harvest (private consultancy), and accumulated exports up to the previous month (MDIC, 2025a).

The calculation of monthly soybean availability was performed in MS Excel®. For January, the annual initial stock was added to the annual production multiplied by the percentage harvested by January 15th. From February to December, the calculation included the initial stock and the soybeans harvested by the 15th of the month, subtracting the accumulated exports of the year up to the previous month. The three resulting state series were submitted to Principal Component Analysis (PCA) to create a single variable, “Factor 1”, aiming to circumvent high multicollinearity.

The second exogenous variable, “Average ship docking time”, measured the operational performance of the Port of Santos. This series, with 180 monthly observations (January 2010 to December 2024), represented the average number of days that solid bulk vessels remained docked for loading. The data were obtained from the Statistical Monthly Report of the Santos Port Authority (APS, 2025a), assuming that longer docking times would indicate operational difficulties.

Exploratory analyses were initiated in MS Excel® and deepened in Python, using libraries such as Pandas, Numpy, Statsmodel, and Matplotlib. The codes were developed with the assistance of Oliveira et al. (2025). For the response variable, descriptive statistics, histograms, boxplots, seasonal decomposition, stationarity tests (ADF and KPSS), ACF, and PACF were performed. The exogenous variables were subjected to univariate and bivariate descriptive analyses with the response variable, using Pearson correlation and scatter plots. Multicollinearity was assessed by Pearson correlation matrices and Variance Inflation Factor (VIF).

For predictive modeling, SARIMA (Seasonal Autoregressive Integrated Moving Average) and SARIMAX (SARIMA with Exogenous Regressors) models were employed. SARIMA models the time series’ dependence on past values and forecast errors, incorporating seasonality, while SARIMAX includes exogenous variables. Non-seasonal and seasonal differencing of order 1 (d=1 and D=1) was applied to the response variable to ensure stationarity. The selection of orders p,d,q and P,D,Q was automated in Python, via the `auto_arima` function (pmdarima), based on the lowest AIC and BIC values.

Six models were tested: one SARIMA (exports series) and five SARIMAX (exogenous variables “Factor 1” and “Average ship docking time”, with different lags). Model comparison was performed with data divided into training (January 2010 to December 2023) and testing (January to June 2024). Evaluation criteria included WAPE (Weighted Absolute Percentage Error), statistical significance of the intercept, exogenous variables, and autoregressive and moving average parameters, and residual analysis for normality, autocorrelation, and heteroscedasticity.

3. Results and Discussion

The study began with a detailed exploratory analysis of the time series of monthly soybean exports through the port of Santos, covering 180 observations from January 2010 to December 2024. Descriptive statistics revealed an average of 1.465 million tons and a median of 0.786 million tons, indicating an asymmetric distribution with a higher concentration in smaller volumes. The standard deviation of 1.582 million tons and the coefficient of variation of 1.080 underscored the high variability of monthly shipments. The interquartile range, from 0.204 to 2.487 million tons, and the minimum (0.000000089 million tons) and maximum (5.943 million tons) values confirmed the presence of many months with exports below the average and a few high peaks, a common characteristic in agricultural commodities.

The analysis of the series’ shape measures, with skewness of 1.0642 and Fisher’s kurtosis of 0.0687, reinforced the observation of a right-skewed distribution, but without excessively heavy tails. This means that, although export volumes are often low, extreme high export events are less likely to occur frequently. This data distribution configuration is crucial for the choice and calibration of predictive models, as it requires approaches that can effectively handle non-normality and variance heterogeneity. Understanding these characteristics was fundamental for the subsequent modeling stage, guiding the selection of appropriate techniques to capture the intrinsic complexity of soybean shipments.

The seasonal decomposition of the time series showed an increasing trend over the analyzed period, reflecting the continuous growth in annual soybean exports. An annual and recurring seasonal pattern, typical of agricultural products, was observed, with export peaks concentrated in specific months of the year, generally after harvest. The decomposition residuals behaved well around zero, but with greater dispersion in specific periods, indicating that, even after removing the trend and seasonality, some residual variability persisted. The presence of a trend and a strong seasonal component suggested the non-stationarity of the series, a finding that, according to Oliveira et al. (2025), is common in economic series and requires differencing to stabilize the mean and variance over time, preparing the data for modeling.

To formally confirm non-stationarity, the Augmented Dickey-Fuller (ADF) Test and the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) Test were applied. The ADF Test, with a null hypothesis of a unit root (non-stationary), resulted in a statistic of -0.6268 and a p-value of 0.8648. At a significance level of 0.05, the null hypothesis could not be rejected, confirming the non-stationarity of the series. In contrast, the KPSS Test, with a null hypothesis of stationarity around a trend, presented a statistic of 0.7974 and a p-value of 0.0100. In this case, the null hypothesis was rejected, corroborating that the series is not stationary around a trend. Both tests, therefore, converged to the conclusion that the monthly soybean export series was non-stationary, validating the need for differencing for modeling.

The analysis of the autocorrelation function (ACF) and partial autocorrelation function (PACF) provided crucial insights into the temporal dependence of the series. The ACF plot indicated a strong positive autocorrelation at the first lag, around 0.75, with a slow decay, a typical behavior of non-stationary series (Oliveira et al., 2025). Positive peaks were also identified at multiple lags of 12 and negative peaks at lags 6 and 18, suggesting a clear annual seasonality. The PACF plot, in turn, detected a strong short-term autoregressive dependence, with the most significant autocorrelation at the first lag. Together, the ACF and PACF results pointed to a low-order autoregressive structure, for both non-seasonal and seasonal components, guiding the choice of initial parameters for the SARIMA and SARIMAX models.

Preparation of the First Exogenous Variable: “Factor 1”

The construction of the first exogenous variable, named “Factor 1 – Soy availability in Mato Grosso, Goiás, and São Paulo”, was motivated by the predominance of these states in the origin of soy exports via the port of Santos. Between 2004 and 2024, on average, 84% of the soy exported by Santos came from Mato Grosso (51%), Goiás (19%), and São Paulo (14%). The analysis of the correlation between annual exports and the summed annual production of these three states revealed a Pearson coefficient of 0.9913, indicating a strong positive relationship. This evidence reinforced the hypothesis that the availability of soy in the producing regions is a determining factor for export volumes. However, the annual nature of the production data required the creation of a monthly proxy for soy availability, in order to align the exogenous variable with the frequency of the export series.

To approximate the monthly availability of soybeans, a specific calculation was developed. For the month of January, the initial annual stock of each state (as of December 31st) was added to the annual production of the ongoing harvest, multiplied by the percentage harvested by January 15th. For the months of February to December, the calculation included the initial annual stock and the soybeans already harvested by the 15th of each month, subtracting the accumulated exports up to the previous month through all Brazilian ports. This method aimed to capture the monthly supply dynamics. An important limitation was the availability of harvested percentage data, which was only accessible from January 2010 onwards. This restriction led to the reduction of the study’s sample to 180 observations, from January 2010 to December 2024, instead of the originally planned series that would have started in 2004.

The three soybean availability variables for Mato Grosso, Goiás, and São Paulo, each with 180 monthly observations, were subjected to univariate descriptive analyses. In all cases, the series presented a right-skewed distribution, an increasing trend, and annual seasonality, patterns similar to those observed in the response variable of exports. This consistency in the characteristics of individual availability series reinforced their relevance as exogenous variables. The similarity in temporal and distributional behaviors suggested that the factors influencing soybean supply in the producing states are intrinsically linked to export movements through the port of Santos, validating their inclusion in predictive modeling.

In the bivariate analysis stage, Pearson correlations between each state availability variable and the response variable were calculated. Mato Grosso presented a correlation of 0.8386, Goiás of 0.7189, and São Paulo of 0.8725, indicating strong positive correlations. However, the multicollinearity assessment among the three exogenous series revealed high correlation coefficients: 0.88 between Mato Grosso and Goiás, 0.78 between Mato Grosso and São Paulo, and 0.62 between Goiás and São Paulo. The Variance Inflation Factor (VIF) for Mato Grosso was 7.214, confirming the presence of moderate to high multicollinearity. This interdependence between variables indicated the need for an approach to reduce data dimensionality and avoid instability issues in predictive models.

To circumvent multicollinearity and synthesize the information from the three state variables, the decision was made to construct a single composite variable using Principal Component Analysis (PCA), following the methodology of Fávero and Belfiore (2017). Initially, a simple sum of the variables was considered, resulting in a correlation of 0.8426 with the response variable. However, the predominance of Mato Grosso (68% of the sample) raised doubts about the representativeness of the simple sum. The Bartlett’s Test of Sphericity, applied to the correlation matrix of the three variables, returned a p-value close to zero, rejecting the null hypothesis of uncorrelated variables and validating the use of PCA for dimensionality reduction.

The eigenvalue analysis of PCA indicated the presence of a dominant factor. The first principal component was the only one with an eigenvalue greater than 1 (2.5194), explaining approximately 84% of the joint variance of the three original variables. The other two components had eigenvalues less than 1 (0.3940 and 0.0866) and contributed marginally (13% and 3%). Based on Kaiser’s criterion, which retains components with eigenvalues greater than unity, only the first factor was selected. Communalities showed that this retained factor explained 94% of the variance of Mato Grosso, 83% of Goiás, and 75% of São Paulo, reinforcing the adequacy of the resulting variable as exogenous. Factor loadings were high and of the same sign (MT: 0.9695; GO: 0.9116; SP: 0.8652), indicating that the variables move in the same direction and contribute significantly to the factor. The resulting series of factor scores was designated as “Factor 1 – Soybean Availability in Mato Grosso, Goiás, and São Paulo”, chosen for its higher correlation with the response variable (0.8824) compared to the simple sum (0.8426).

Second Exogenous Variable: “Average Ship Turnaround Time”

The second exogenous variable, “Average ship turnaround time”, consisted of the average number of days that solid bulk ships remained docked at the port of Santos for loading, with 180 monthly observations from January 2010 to December 2024. This variable was selected as a measure of port operational performance, based on the premise that longer turnaround times could indicate operational difficulties and, consequently, negatively impact export volume. Exploratory analysis revealed an average of 3.325 days, a median of 3.200 days, a standard deviation of 0.493 days, and an interquartile range of 3 to 3.725 days, with a minimum of 2.500 and a maximum of 5.200 days. These values indicated relatively low variability and a distribution concentrated around the mean.

The shape measures for “Average ship docking time”, with a skewness of 0.896 and a Fisher kurtosis of 0.877, indicated a right-skewed distribution, suggesting the occasional occurrence of longer docking times. However, the probability of extreme events was considered low. The Pearson correlation between this variable and the response variable (monthly soybean exports) was -0.2554. The negative sign was aligned with the expectation that better port performance (shorter docking time) would be associated with higher export volumes. Nevertheless, the low magnitude of the correlation served as a warning, indicating that the variable might not present statistical significance in the SARIMAX models, either alone or in combination with “Factor 1”, which was a crucial point in the evaluation of the predictive models.

Prediction Models: SARIMA and SARIMAX

For the development of the forecasting tool, the SARIMA and SARIMAX models were used, both derived from ARIMA, which models autoregressive (AR), integrated (I), and moving average (MA) components. SARIMA incorporates the seasonality (P, D, Q) present in agricultural exports, while SARIMAX adds exogenous variables (X) to improve the fit. Non-seasonal (d=1) and seasonal (D=1) differencing of order 1 was applied to the response variable to ensure stationarity, as indicated by exploratory analysis. The selection of orders p,d,q and P,D,Q for the models was performed automatically by the `auto_arima` function from the `pmdarima` library in Python, which seeks the lowest AIC and BIC values, balancing model complexity and data fitting capability.

Six models were tested: one SARIMA and five SARIMAX, to forecast monthly soybean exports in the first semester of 2024. The data were divided into a training period (January 2010 to December 2023) and a testing period (January to June 2024). The SARIMAX models included “Factor 1” with lags of zero, one, and two months, “Average ship docking time” without lag, and a combination of “Factor 1” with two months lag and “Average ship docking time” without lag. Model comparison was based on the Weighted Absolute Percentage Error (WAPE), statistical significance of parameters, residual analysis (normality, autocorrelation, and heteroscedasticity), and AIC and BIC values. MAPE was discarded due to distortion caused by values close to zero in the response variable.

The SARIMA model, which considered only the export time series, obtained a WAPE of 7.42%. This result indicated good predictive performance, with the intercept and the autoregressive and moving average parameters being statistically significant at the 5% level. The residual analysis, through the Ljung-Box Test, did not detect residual autocorrelation at lags of 12 and 24 periods, suggesting that the residuals were white noise. The Harvey Test did not reject the hypothesis of constant variance (homoscedasticity). However, the Jarque-Bera Test indicated that the distribution of the residuals did not adhere to normality, suggesting that the model, although effective, did not capture all the complexity of the analyzed time series, in line with observations by Oliveira et al. (2025).

The SARIMAX models presented varied results. SARIMAX 1, with “Factor 1” without lag, resulted in a WAPE of 16.643%, worsening the prediction compared to SARIMA. SARIMAX 2, with “Factor 1” lagged by one month, improved the WAPE to 9.585%, but was discarded due to residual autocorrelation at lag 12 and the statistical insignificance of the intercept. SARIMAX 3, with “Factor 1” lagged by two months, achieved a WAPE of 8.280% and passed the other criteria, except for the residuals not adhering to normality. SARIMAX 4, which used “Average ship docking time” without lag, obtained a WAPE of 7.630%, outperforming the models with “Factor 1”, but the exogenous variable was not statistically significant, indicating that it did not add relevant predictive information.

The SARIMAX 5, which combined “Factor 1” with a two-month lag and “Average ship docking time” without lag, presented a WAPE of 8.730%. In this model, the docking time variable remained without statistical significance. Furthermore, the Ljung-Box Test detected autocorrelation of the residuals at a lag of 12 periods, and the Jarque-Bera Test indicated that the residuals did not adhere to normality. The overall comparison of the six models indicated that SARIMA and SARIMAX 3 were the best performing. Both models presented non-seasonal orders (0,0,2), with no autoregressive terms or differencing, only errors from the previous two periods. The seasonal orders were also identical (2,1,0), with two seasonal autoregressive terms (12 and 24 months) and one seasonal differencing, with no seasonal moving average terms.

Despite the great similarity in AIC and BIC values between SARIMA (237,173 and 255,472) and SARIMAX 3 (235,132 and 256,381), SARIMA was considered the most suitable model for prediction due to its slightly lower WAPE of 7.42% compared to SARIMAX 3’s 8.28%. The choice was also influenced by the fact that the exogenous variable “Factor 1” did not consistently contribute to improved accuracy. The predictions of both models for the first half of 2024 were quite close to the actual export volumes in the months of February, March, April, and May. However, the models failed to predict January, a transition month with traditionally low volumes, and June, where the predictions diverged from the actual values, especially in SARIMAX 3. The export in June 2024 being lower than in May was an anomaly, as historically the difference between these months varied between 38.6% and 54%.

In summary, the SARIMA and SARIMAX models demonstrated satisfactory results with potential for practical application in predicting monthly soybean exports through the port of Santos, especially from February to May. Although the SARIMA model stood out as the most robust among those tested, the non-adherence of the residuals to a normal distribution, according to the Jarque-Bera Test, indicates that the model did not capture the full complexity of the series. The limited contribution of the selected exogenous variables to consistently improve predictive accuracy, especially in January and June, suggests the need to incorporate more representative exogenous variables of export dynamics, such as the pace of trade, domestic and international demand, prices, and the activity of competing ports, for future improvements and a more precise fit.

4. Conclusion

The study aimed to develop a predictive model for monthly soybean shipments through the port of Santos, focusing on the first semester of the year, to aid in logistical planning. Through a detailed analysis of the time series between January 2010 and December 2024, high variability, asymmetry, an upward trend, and strong seasonality were found in the export data. The non-stationarity of the series was formally confirmed, requiring differencing for modeling. Two exogenous variables were constructed: a synthetic one for soybean availability in the main producing states (Factor 1, via Principal Component Factor Analysis) and another for port operational performance (average ship berthing time). After testing six models, the SARIMA model demonstrated the best predictive performance, with a Weighted Absolute Percentage Error of 7.42%, outperforming SARIMAX combinations. This model proved effective in forecasting export volumes between February and May, offering a valuable tool for planning and decision-making in agricultural market consultancies by providing an improved understanding of the dynamics of soybean exports through the São Paulo port.

Despite the satisfactory performance of the SARIMA model, it was identified that the predictive accuracy was less consistent in the months of January and June, and the model’s residuals did not adhere to the normal distribution, indicating that the series’ total complexity was not fully captured. The exogenous variables tested, although methodologically well-constructed, did not consistently contribute to improving prediction accuracy, suggesting the need to incorporate factors more representative of export dynamics. For future studies, the inclusion of additional exogenous variables is recommended, such as the pace of commercialization, domestic and external demand, market prices, and the activity of competing ports. Furthermore, exploring more robust indicators of port performance, such as maximum operational capacity and ship waiting time offshore, can significantly enhance the predictive capability of the models.

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