# Time Series Prediction with Artificial Neural Networks: An Analysis Using Brazilian Soybean Production

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## Abstract

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## 1. Introduction

#### 1.1. Artificial Neural Networks

- Can soybean harvest area, yield, and production be predicted efficiently using Artificial Neural Networks?
- If so, are Artificial Neural Networks more effective than classical methods of Time Series Analysis to predict soybean production measures?

#### 1.2. Time Series and Classical Methods

## 2. Materials and Methods

#### 2.1. Dataset

#### 2.2. Model Classification

## 3. Results and Discussion

#### 3.1. Time Series Analysis Using Classical Predictive Methods (Functions)

#### 3.1.1. Harvested Area

#### 3.1.2. Yield

#### 3.1.3. Production

#### 3.2. ANN Model

#### 3.2.1. Training, Validation, and Testing of Neural Network

#### 3.2.2. Time Series Results with an Artificial Neural Network

#### 3.2.3. Comparison between Artificial Neural Networks and Time Series Classical Models

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Method | Formulas | Features |
---|---|---|

Linear function | $y=ax\pm b$ | Linear is defined as a curve of the first degree or a simple straight line—where y is the trend, x represents the period of time, a is a slope, and b is the intercept. The intercept will determine how far from the x-axis the trend begins. The slope will determine the direction and the steepness. |

Exponential function | $y=a{e}^{bx}$ | Exponential is defined as a transcendental curve, where e represents the basis for natural logarithms, and its constant value is 2.7813. It grows exponentially, but they never reach the attracting value. |

Logarithmic function | $y=aln\left(x\right)\pm b$ | The inverse of the exponential function is a logarithmic function. |

Polynomial function | $y=a{x}^{2}\pm bx\pm c$ | The second-degree polynomial curve is a parabola. The polynomial model can go up to the sixth degree. A larger magnitude corresponds to a greater adjustment than that in the original data; however, this does not mean that it is best for forecasting. The best method is the one that can perform well with minimum parameters. |

Power function | $y=a{x}^{b}$ | The graph of a power curve is a hyperbola. |

Model | Trend Formulas |
---|---|

Linear function | $y=0.5523x-1.1485$ |

Exponential function | $y={2.1503e}^{0.0582x}$ |

Logarithmic function | $y=7.8508ln\left(x\right)-10.379$ |

Polynomial function | $y={0.009x}^{2}+0.0937x+2.8259$ |

Power function | $y={0.4302x}^{1.0419}$ |

Model | Trend Formulas |
---|---|

Linear function | $y=0.0388x+1.0523$ |

Exponential function | $y={1.1748e}^{0.0199x}$ |

Logarithmic function | $y=0.5735ln\left(x\right)+0.3397$ |

Polynomial function | $y={0.0001x}^{2}+0.0321x+1.111$ |

Power function | $y={0.7747x}^{0.3113}$ |

Model | Trend Formulas |
---|---|

Linear function | $y=1.6935x-12.323$ |

Exponential function | $y={2.5259e}^{0.0782x}$ |

Logarithmic function | $y=22.599ln\left(x\right)-36.247$ |

Polynomial function | $y={0.045x}^{2}-0.6007x+7.5607$ |

Power function | $y={0.3332x}^{1.3534}$ |

Rank | Model | R | MAE | MSE |
---|---|---|---|---|

${1}^{\circ}$ | Polynomial function | 0.944 | 1.813 | 3.915 |

${2}^{\circ}$ | Power function | 0.949 | 1.927 | 6.901 |

${3}^{\circ}$ | Linear function | 0.904 | 1.996 | 6.716 |

${4}^{\circ}$ | Exponential function | 0.797 | 2.481 | 8.859 |

${5}^{\circ}$ | Logarithmic function | 0.680 | 3.825 | 22.482 |

Rank | Model | R | MAE | MSE |
---|---|---|---|---|

${1}^{\circ}$ | Linear function | 0.898 | 0.148 | 0.036 |

${2}^{\circ}$ | Polynomial function | 0.899 | 0.158 | 0.037 |

${3}^{\circ}$ | Exponential function | 0.874 | 0.170 | 0.038 |

${4}^{\circ}$ | Power function | 0.794 | 0.202 | 0.068 |

${5}^{\circ}$ | Logarithmic function | 0.728 | 0.239 | 0.095 |

Rank | Model | R | MAE | MSE |
---|---|---|---|---|

${1}^{\circ}$ | Polynomial function | 0.968 | 3.990 | 21.755 |

${2}^{\circ}$ | Power function | 0.952 | 6.058 | 88.784 |

${3}^{\circ}$ | Exponential function | 0.853 | 5.847 | 77.116 |

${4}^{\circ}$ | Linear function | 0.867 | 7.658 | 91.879 |

${5}^{\circ}$ | Logarithmic function | 0.574 | 13.843 | 293.441 |

Rank | Model | R | MAE | MSE |
---|---|---|---|---|

${1}^{\circ}$ | ANN | 0.995 | 1.309 | 2.763 |

${2}^{\circ}$ | Polynomial function | 0.944 | 1.813 | 3.915 |

${3}^{\circ}$ | Power function | 0.949 | 1.927 | 6.901 |

${4}^{\circ}$ | Linear function | 0.904 | 1.996 | 6.716 |

${5}^{\circ}$ | Exponential function | 0.797 | 2.481 | 8.859 |

${6}^{\circ}$ | Logarithmic function | 0.680 | 3.825 | 22.482 |

Rank | Model | R | MAE | MSE |
---|---|---|---|---|

${1}^{\circ}$ | Linear function | 0.898 | 0.148 | 0.036 |

${2}^{\circ}$ | Polynomial function | 0.899 | 0.158 | 0.037 |

${3}^{\circ}$ | ANN | 0.954 | 0.220 | 0.084 |

${4}^{\circ}$ | Exponential function | 0.874 | 0.170 | 0.038 |

${5}^{\circ}$ | Power function | 0.794 | 0.202 | 0.068 |

${6}^{\circ}$ | Logarithmic function | 0.728 | 0.239 | 0.095 |

Rank | Model | R | MAE | MSE |
---|---|---|---|---|

${1}^{\circ}$ | ANN | 0.992 | 3.362 | 19.713 |

${2}^{\circ}$ | Polynomial function | 0.968 | 3.990 | 21.755 |

${3}^{\circ}$ | Power function | 0.952 | 6.058 | 88.784 |

${4}^{\circ}$ | Exponential function | 0.853 | 5.847 | 77.116 |

${5}^{\circ}$ | Linear function | 0.867 | 7.658 | 91.879 |

${6}^{\circ}$ | Logarithmic function | 0.574 | 13.843 | 293.441 |

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**MDPI and ACS Style**

Abraham, E.R.; Mendes dos Reis, J.G.; Vendrametto, O.; Oliveira Costa Neto, P.L.d.; Carlo Toloi, R.; Souza, A.E.d.; Oliveira Morais, M.d.
Time Series Prediction with Artificial Neural Networks: An Analysis Using Brazilian Soybean Production. *Agriculture* **2020**, *10*, 475.
https://doi.org/10.3390/agriculture10100475

**AMA Style**

Abraham ER, Mendes dos Reis JG, Vendrametto O, Oliveira Costa Neto PLd, Carlo Toloi R, Souza AEd, Oliveira Morais Md.
Time Series Prediction with Artificial Neural Networks: An Analysis Using Brazilian Soybean Production. *Agriculture*. 2020; 10(10):475.
https://doi.org/10.3390/agriculture10100475

**Chicago/Turabian Style**

Abraham, Emerson Rodolfo, João Gilberto Mendes dos Reis, Oduvaldo Vendrametto, Pedro Luiz de Oliveira Costa Neto, Rodrigo Carlo Toloi, Aguinaldo Eduardo de Souza, and Marcos de Oliveira Morais.
2020. "Time Series Prediction with Artificial Neural Networks: An Analysis Using Brazilian Soybean Production" *Agriculture* 10, no. 10: 475.
https://doi.org/10.3390/agriculture10100475