# Forecasting the S&P 500 Index Using Mathematical-Based Sentiment Analysis and Deep Learning Models: A FinBERT Transformer Model and LSTM

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Methodologies for Sentiment Analysis

#### 2.2. Stock Market and Sentiment Analysis

## 3. Data Description

#### New York Times Data and S&P 500 Index

## 4. Methods

#### 4.1. News Sentiment Analysis

#### 4.2. LSTM

#### 4.3. FinBERT

## 5. Empirical Results

#### 5.1. Hyperparameter Tuning

#### 5.2. Error Measure

#### 5.3. Summary Results

#### 5.4. Model Performance in Crisis Periods

## 6. Discussion

## 7. Concluding Remarks

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. The Choice of Optimal Lag

Lag | Model | MSE | RMSE | MAE | ${\mathit{R}}^{2}$ |
---|---|---|---|---|---|

1 | LSTM-Only | 0.0062 | 0.0791 | 0.0703 | 0.60 |

1 | LSTM-NYT | 0.0019 | 0.0443 | 0.0361 | 0.87 |

5 | LSTM-Only | 0.0139 | 0.1182 | 0.1086 | 0.11 |

5 | LSTM-NYT | 0.0159 | 0.1262 | 0.1143 | 0.00 |

10 | LSTM-Only | 0.0068 | 0.0829 | 0.0700 | 0.56 |

10 | LSTM-NYT | 0.0056 | 0.0753 | 0.0666 | 0.64 |

## Appendix B. Comparison with Other ML Models

Model | MSE | RMSE | MAE | ${\mathit{R}}^{2}$ | |
---|---|---|---|---|---|

Gradient Boosting | LSTM-Only | 0.0011 | 0.0191 | 0.0159 | 0.4651 |

LSTM-NYT | 0.0011 | 0.0192 | 0.0160 | 0.4654 | |

XGBoost | LSTM-Only | 0.0011 | 0.0204 | 0.0169 | 0.4437 |

LSTM-NYT | 0.0011 | 0.0205 | 0.0169 | 0.4388 | |

AdaBoost | LSTM-Only | 0.0019 | 0.0275 | 0.0239 | 0.0323 |

LSTM-NYT | 0.0019 | 0.0273 | 0.0238 | 0.0495 |

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Period: 1 January 2018–31 December 2022 (1259 Days) | |||||
---|---|---|---|---|---|

Mean | Max. | Min. | Std. Dev. | Skewness | Kurtosis |

3449.73 | 4796.56 | 2237.4 | 668.91 | 0.36 | −1.28 |

Labels | Positive | Neutral | Negative | Total |
---|---|---|---|---|

ratio | 8.05% | 27.9% | 64.05% | 30,797 |

**Table 3.**Summary statistics for the daily sentiment score for The New York Times. The Jarque–Bera statistic was used to test the null hypothesis of normality for the sample returns. ${}^{\u2021}$ indicates a rejection of the null hypothesis at the $1\%$ significance level.

Sectors | Mean | Max. | Min. | Std. Dev. | Skewness | Kurtosis | Jarque–Bera |
---|---|---|---|---|---|---|---|

Score | −0.18 | 1.0 | −0.99 | 0.52 | −0.03 | −0.09 | 18.53 ${}^{\u2021}$ |

Parameter | Grid |
---|---|

units | [32, 64, 128, 256] |

dropout_rate | [0.1, 0.2, 0.3, 0.4, 0.5], |

optimizer | [Adam Nadam, RMSprop, SGD] |

activation | [ReLU, tanh, SELU, ELU, Swish] |

learning_rate | [0.001, 0.01, 0.1] |

epochs | [50, 100, 150] |

batch_size | [16, 32, 64] |

Evaluation Measure | MSE | RMSE | MAE | ${\mathit{R}}^{2}$ |
---|---|---|---|---|

LSTM-Only | 0.0026 | 0.0513 | 0.0394 | 0.8339 |

LSTM-NYT | 0.0016 | 0.0407 | 0.0313 | 0.8950 |

Samples | N | Mean | Std. Dev. | t-Statistic | p-Value |
---|---|---|---|---|---|

LSTM-Only | 365 | 0.814 | 0.114 | 2.255 | 0.024 |

LSTM-NYT | 365 | 0.795 | 0.123 |

Evaluation Measure | MSE | RMSE | MAE | ${\mathit{R}}^{2}$ |
---|---|---|---|---|

LSTM-Only | 0.004 | 0.064 | 0.055 | 0.771 |

LSTM-NYT | 0.002 | 0.051 | 0.042 | 0.851 |

Evaluation Measure | MSE | RMSE | MAE | ${\mathit{R}}^{2}$ |
---|---|---|---|---|

LSTM-Only | 0.003 | 0.059 | 0.047 | 0.623 |

LSTM-NYT | 0.002 | 0.045 | 0.036 | 0.778 |

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## Share and Cite

**MDPI and ACS Style**

Kim, J.; Kim, H.-S.; Choi, S.-Y.
Forecasting the S&P 500 Index Using Mathematical-Based Sentiment Analysis and Deep Learning Models: A FinBERT Transformer Model and LSTM. *Axioms* **2023**, *12*, 835.
https://doi.org/10.3390/axioms12090835

**AMA Style**

Kim J, Kim H-S, Choi S-Y.
Forecasting the S&P 500 Index Using Mathematical-Based Sentiment Analysis and Deep Learning Models: A FinBERT Transformer Model and LSTM. *Axioms*. 2023; 12(9):835.
https://doi.org/10.3390/axioms12090835

**Chicago/Turabian Style**

Kim, Jihwan, Hui-Sang Kim, and Sun-Yong Choi.
2023. "Forecasting the S&P 500 Index Using Mathematical-Based Sentiment Analysis and Deep Learning Models: A FinBERT Transformer Model and LSTM" *Axioms* 12, no. 9: 835.
https://doi.org/10.3390/axioms12090835