# A Novel Implementation of Siamese Type Neural Networks in Predicting Rare Fluctuations in Financial Time Series

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## Abstract

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## 1. Introduction

#### 1.1. Literature Review on Classification of Tabular Data Using CNNs

#### 1.2. Motivation

## 2. Materials and Methods

#### 2.1. A Brief Mathematical Survey on Financial Analytics

- $\theta =1$, where a short-term upward share movement is expected:$$d{X}_{t}=(B+{\mathsf{\Lambda}}^{2}-\frac{1}{2}{\sigma}_{t}^{2})\phantom{\rule{0.166667em}{0ex}}dt+{\sigma}_{t}\phantom{\rule{0.166667em}{0ex}}d{W}_{t}.$$
- $\theta =0$, where not much short-term share movement is expected:$$d{X}_{t}=(B-\frac{1}{2}{\sigma}_{t}^{2})\phantom{\rule{0.166667em}{0ex}}dt+{\sigma}_{t}\phantom{\rule{0.166667em}{0ex}}d{W}_{t}.$$
- $\theta =-1$, where a short-term downward share movement is expected:$$d{X}_{t}=(B-\frac{1}{2}{\sigma}_{t}^{2})\phantom{\rule{0.166667em}{0ex}}dt+{\sigma}_{t}\phantom{\rule{0.166667em}{0ex}}d{W}_{t}+\rho \phantom{\rule{0.166667em}{0ex}}d{Z}_{\lambda t}.$$

#### 2.2. Materials: Data

- We collect High, Low and Close price for a 25 day period. This results in tabular data that can be arranged in a $25\times 3$ matrix. The columns of this matrix represent the High, Low and Close price of the day and the ith row of the matrix represents the ith day in the 25 day window.
- The values across each row are converted to an 8 bit integer between 0 and 255 and stored in the vector ${\overrightarrow{V}}_{25\times 3}$ below.$${\overrightarrow{V}}_{25\times 3}=\left[\begin{array}{c}{v}_{1}\\ {v}_{2}\\ \vdots \\ {v}_{i}\\ \vdots \\ {v}_{25}\end{array}\right]$$
- We then arrange the ${v}_{i}$’s in a way that allows us to represent the temporal relationship spatially.$${M}_{5\times 5}=\left[\begin{array}{ccccc}{v}_{1}& {v}_{2}& {v}_{3}& {v}_{4}& {v}_{5}\\ {v}_{10}& {v}_{9}& {v}_{8}& {v}_{7}& {v}_{6}\\ {v}_{11}& {v}_{12}& {v}_{13}& {v}_{14}& {v}_{15}\\ {v}_{20}& {v}_{19}& {v}_{18}& {v}_{17}& {v}_{16}\\ {v}_{21}& {v}_{22}& {v}_{23}& {v}_{24}& {v}_{25}\end{array}\right]$$
- This allows us to create an image corresponding to the matrix ${M}_{5\times 5}$ as shown in Figure 1 below.

#### 2.3. Methods

## 3. Results

## 4. Discussion

- Limited data resulting in production of limited images
- Extreme class imbalance (99-1, 95-5, 90-10) as is common with rare event prediction.

- image size, class imbalance level and training and testing split ratios were varied
- Principal Component Analysis (PCA) on the $M\times 4096$ matrix before training and testing was performed
- different types of re-sampling techniques were used and
- hyperparameter variations were considered.

## 5. Conclusions

- The first is that an active learning approach (Malialis et al. 2020) can be applied to this method in which after every day, the two bootstraps are retaken to include the new observation. While this method may be computationally expensive, it could lead to a more pronounced separation in the event/event and event/non-event distributions, thereby leading to better predictions.
- In this paper we proposed a “snake" method to transform time series into images. Since there a variety of ways to visualize tabular data as an image (Hatami et al. 2017; Sezer and Ozbayoglu 2018; Sharma et al. 2019; Sharma and Kumar 2020a; Sun et al. 2019), we note this as a means to parameterize or tune our method for other future applications. For instance, the research presented in this paper made use of square images. However, one could consider circular images (Wang and Oates 2015), textured images (Sharma and Kumar 2020b) or images created through Markov Transition Field (MTF) (Wang and Oates 2015). Further research can be done to compare image shape or similarly develop new transformation techniques that result in other types of images.
- We believe different image classification frameworks such as ResNet50 (https://arxiv.org/abs/1512.03385, accessed on 7 November 2021) can be experimented with to further improve results as they can effect the image resizing as well as the output feature vector that is used for similarity comparisons.
- For this research we used time series data from only the S&P 500 index. The combination of S&P 500 with other time series data such as Dow Jones (https://finance.yahoo.com/quote/%5EDJI/, accessed on 7 November 2021) or Nasdaq (https://finance.yahoo.com/quote/%5EIXIC/, accessed on 7 November 2021) could help to identify further patterns to improve prediction accuracy, or related derived metrics such as volatility indexes.
- Lastly, although this paper investigated daily financial time series data (HLC) to predict and identify patterns for rare event prediction, the proposed approach could also be applied to intra-day trading applications as technical analyses are even more relevant there.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Corresponding image reconstructions of the time series in Figure 2.

**Table 1.**Comparing performance metrics in the test data set across all image sizes and class imbalance ratios.

Image Size | Class Imbalance | Accuracy | Precision | Recall | ${\mathit{F}}_{1}$ Score |
---|---|---|---|---|---|

5 × 5 | 1% | 0.691 | 0.010 | 0.364 | 0.020 |

5% | 0.763 | 0.024 | 0.105 | 0.039 | |

10% | 0.819 | 0.086 | 0.109 | 0.096 | |

6 × 6 | 1% | 0.687 | 0.005 | 0.182 | 0.010 |

5% | 0.776 | 0.041 | 0.179 | 0.067 | |

10% | 0.808 | 0.083 | 0.121 | 0.098 | |

7 × 7 | 1% | 0.580 | 0.008 | 0.364 | 0.015 |

5% | 0.795 | 0.067 | 0.259 | 0.106 | |

10% | 0.826 | 0.131 | 0.159 | 0.144 | |

8 × 8 | 1% | 0.678 | 0.008 | 0.273 | 0.015 |

5% | 0.708 | 0.048 | 0.267 | 0.082 | |

10% | 0.707 | 0.086 | 0.239 | 0.127 | |

9 × 9 | 1% | 0.765 | 0.011 | 0.273 | 0.021 |

5% | 0.782 | 0.044 | 0.167 | 0.070 | |

10% | 0.835 | 0.123 | 0.138 | 0.130 |

Image Size | Imbalance | Event Images | Non-Event Images | Total |
---|---|---|---|---|

$5\times 5$ | 1% | 11 | 1235 | 1246 |

5% | 57 | 1189 | ||

10% | 110 | 1136 | ||

$6\times 6$ | 1% | 11 | 1230 | 1241 |

5% | 56 | 1185 | ||

10% | 107 | 1134 | ||

$7\times 7$ | 1% | 11 | 1216 | 1227 |

5% | 58 | 1169 | ||

10% | 113 | 1114 | ||

$8\times 8$ | 1% | 11 | 1216 | 1227 |

5% | 60 | 1167 | ||

10% | 109 | 1118 | ||

$9\times 9$ | 1% | 11 | 1207 | 1219 |

5% | 60 | 1158 | ||

10% | 109 | 1110 |

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**MDPI and ACS Style**

Basu, T.; Menzer, O.; Ward, J.; SenGupta, I.
A Novel Implementation of Siamese Type Neural Networks in Predicting Rare Fluctuations in Financial Time Series. *Risks* **2022**, *10*, 39.
https://doi.org/10.3390/risks10020039

**AMA Style**

Basu T, Menzer O, Ward J, SenGupta I.
A Novel Implementation of Siamese Type Neural Networks in Predicting Rare Fluctuations in Financial Time Series. *Risks*. 2022; 10(2):39.
https://doi.org/10.3390/risks10020039

**Chicago/Turabian Style**

Basu, Treena, Olaf Menzer, Joshua Ward, and Indranil SenGupta.
2022. "A Novel Implementation of Siamese Type Neural Networks in Predicting Rare Fluctuations in Financial Time Series" *Risks* 10, no. 2: 39.
https://doi.org/10.3390/risks10020039