# Methods for Mid-Term Forecasting of Crop Export and Production
## 5 Discussion and Conclusions  
This paper proposes several neural network models for mid-term forecasting of crop production and export and the approach to regularize them.  
Our collected data set on the world's 15 largest exporters with heterogeneous features such as trade, macro-economic indicators of these countries, yields, and fuel prices could be as a basis for a comprehensive assessment of the global grain market, both in terms of export opportunities and more complete use of the resource potential for grain production.  
The experiments show that the proposed NARX and Transformer models with regularization could be prospective methods for accurate prediction of crop production and export. It was also revealed that vegetation indexes and fuel prices are crucial for export prediction. Still, the fuel prices seem to be more important for predicting production than the NDVI indexes from past observations. We believe that good past NDVIIs mean rich yield and stocks in those years, which could be used for export in the present or future. At the same time, the relationship between the past and future levels of NDVIIs cannot be revealed with the models we tested. The experiments with the textual features show that they help increase trade flows prediction accuracy, but they could not improve the results of predicting production level. It seems that better results can be achieved when we consider different languages and vary messages depending on the importance of their sources.  
The remaining errors of the export and production forecasting can be explained by ignoring some essential features. We plan to consider logistical and infrastructure conditions, climate indicators, and technological features in future research. The latter is a challenging problem, especially for large countries, where conditions vary significantly from region to region. In that case, representations of those features should reflect that variance, but keep low dimensionality to prevent the prediction models from overfitting.  
Conceptualization and methodology, Y.O.; investigation and validation, D.D.; writing-review and editing, D.D. and Y.O. All authors have read and agreed to the published version of the manuscript.  
The study was financially supported by the Ministry of Education and Science of the Russian Federation (agreement no. 075-15-2020-805 from 2 October 2020).  
The data is available on [[http://keen.isa.ru/wheat_dataset](http://keen.isa.ru/wheat_dataset)]([http://keen.isa.ru/wheat_dataset](http://keen.isa.ru/wheat_dataset)) (accessed on 29 September 2021).  
The authors declare no conflict of interest the results.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Features** & \multicolumn{2}{c}{**ALL**} & \multicolumn{2}{c}{**ALL + SE**} & \multicolumn{2}{c}{**ALL + SE + SENTIMENT**} \\ \hline
**Models** & \(\boldsymbol{MSE_{\text{,}}\times 10^{9}}\) & \(\boldsymbol{RMSE}\) & \(\boldsymbol{MSE_{\text{,}}\times 10^{9}}\) & \(\boldsymbol{RMSE}\) & \(\boldsymbol{MSE_{\text{,}}\times 10^{10}}\) & \(\boldsymbol{RMSE}\) \\ \hline
**GRU** & \(1.80\pm 0.47\) & \(0.15\pm 0.07\) & \(\boldsymbol{1.43\pm 0.49}\) & \(\boldsymbol{0.13\pm 0.08}\) & \(1.14\pm 0.10\) & \(0.39\pm 0.11\) \\ \hline
**LSTM** & \(3.76\pm 0.41\) & \(0.22\pm 0.07\) & \(1.69\pm 0.34\) & \(0.15\pm 0.07\) & \(1.26\pm 0.13\) & \(0.41\pm 0.13\) \\ \hline
**SimpleRNN** & \(1.81\pm 0.30\) & \(0.15\pm 0.06\) & \(1.87\pm 0.18\) & \(0.16\pm 0.04\) & \(\boldsymbol{1.02\pm 0.12}\) & \(\boldsymbol{0.37\pm 0.13}\) \\ \hline
**NARX** & \(1.83\pm 0.29\) & \(0.15\pm 0.06\) & \(1.93\pm 0.60\) & \(0.16\pm 0.09\) & \(1.23\pm 0.58\) & \(0.40\pm 0.27\) \\ \hline
**Transformer** & \(\boldsymbol{1.77\pm 0.34}\) & \(\boldsymbol{0.15\pm 0.06}\) & \(1.64\pm 0.42\) & \(0.14\pm 0.07\) & \(1.14\pm 0.12\) & \(0.39\pm 0.13\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Production prediction scores (regularization and sentiment features).