Ensemble Learning with an Adversarial Hypergraph Model and a Convolutional Neural Network to Forecast Stock Price Variations

2.1 GNN for price prediction

Attempts have been made by researchers to express stock relations as graphs in order to train GNNs to learn stock representations [10]. To acquire knowledge on shareholding information, a hybrid technique consisting of Graph Convolutional Networks (GCN) and Long Short-Term Memory (LSTM) was utilized. Subsequently, the study by Xiong et al. [11] a multi-graph convolution network was utilized to forecast stock value variations. This network gave equal weight to graphs that depicted stock ownership, industry, and news links.

In light of recent recommendations made by academics, it has been suggested that the correlations between stock prices and other pertinent data can be depicted using a variety of graphs. The study by Guo [12] a diversified graph was constructed by making use of data at the event level as well as contextual information for the goal of forecasting stock performance. Singh et al. [13] proved that hypergraphs can capture complicated relationships between stocks on a group level of data. The study utilized a hypergraph convolutional network to accurately represent the relationship between fund-holding and business activities and stock volatility. In addition to the financial industry, hypergraph neural networks have demonstrated their usefulness. Their expertise in the disciplines of recommendation and learning analytics was demonstrated in multiple studies that were conducted recently, including [14, 15]. These studies provide valuable insights for readers seeking to observe the application of hypergraph modelling in diverse businesses and broader contexts.

While the aforementioned financial prediction approaches proved to be effective, most of them relied on recurrent neural network (RNN) models that just utilized historical stock price data to generate new price embeddings. Subsequently, employing GCN or an alternative graph neural network, the revised embedding can be subjected to further analysis alongside additional components, such as news [16], industry [17], or shareholder information [18]. In addition, it is worth considering affiliated enterprises [19]. However, the post-processing was conducted at an inconvenient moment. These approaches were limited since they depended on RNN as a starting point and could only capture pairwise connections between stocks. They assumed that all other historical data is linear or steady. Previous hypergraph models disregarded these specific pairwise characteristics while overemphasizing group-level interactions [20].

Furthermore, it is worth noting that none of these research studies fully addressed the issue of overfitting, which in this particular scenario is produced by the constantly shifting market conditions.

2.2 Adversarial training

Significant focus has lately been placed on it [21], as it is undoubtedly the most efficient approach for enhancing model generalization by "protecting" against distorted data. Even when confronted with adversarial attacks, the major goal of adversarial training is to ensure that models continue to generate accurate results while preserving their consistency. This can be accomplished through the combination of negative examples and clean data. Managing overfitting resulting from the market's erratic and ever-changing characteristics is necessary for forecasting stock price fluctuations. In the study by Singh and Malhotra [22], adversarial training on commercial interval insights was performed, and the random characteristics of stock features were successfully recreated. Specifically, Chawla and Walia [23] introduced a sentiment-guided generative adversarial network to address the topic of stock prediction. With the goal of achieving results that are competitive, Jaswal et al. [24] integrated adversarial training with transfer learning.

2.3 Ensemble learning for price prediction

Convolutional neural networks, often known as CNNs, are currently being utilized in the study of price forecasting to improve the accuracy of classification or regression by applying deep learning techniques. In the analysis of financial time series, the research carried out by the study of Baghel et al. [25] showed that the combined models had excellent performance compared to the separate models they were compared to. Using denoising autoencoders (SDAE) with bootstrap aggregation (bagging), as proposed by Singh and Malhotra [26], is one method for accurately depicting the intricate interrelationships between oil price and its variables. To forecast the S&P 500 index, this study used a combination of ensemble learning and two RNNs in the study by Chen et al. [27]. The framework for forecasting stock indexes established by the study of Ye et al. [28] included four tree-based ensemble algorithms: XGBoost, LightGBM, vanilla RNN, bidirectional RNN, LSTM, and gated recurrent unit (GRU).

Standard training may lead to overfitting in the dynamic financial market with stochastic price movements. So, the research questions are:

Question 1: Is it possible to improve stock price forecasts by collecting complicated business data?

Question 2: How can we make the model more resilient without lowering its accuracy in prediction?

To answer the questions, combining hypergraph convolution and essential grid learning can effectively detect complicated linkages across identical stocks while addressing stock stochasticity via adversarial training. This approach has promise for addressing the aforementioned inquiries. In contrast to alternative approaches that initially employ recurrent neural networks (RNNs), the authors demonstrated the efficacy of integrating supplementary information, such as industry data, through a Graph Convolutional Network (GCN) prior to utilizing RNNs. This enables Recurrent Neural Networks (RNNs) to comprehend the enduring interdependencies of pairwise relationships among comparable organizations in the future.

4.1 Experimental setup

The authors employ their dataset for data gathering to provide an equitable comparison with study by Qin et al. [38]. From April 1, 2013, to March 31, 2019, the Chinese A-share market had 758 shares for regular trading. The authors will validate technique by collecting data from other markets, such as the United States or Europe. In the dataset, each stock is represented by one of the six parameters that are listed below: the initial price, the closing price, the trading volume, the value, and the highest and lowest prices. After implementing the min-max normalization approach for each stock input feature independently, the results were displayed. In the case that trade data for specific shares is unavailable during the suspension period, the price attributes from the previous day will be applied regardless of the situation. According to the information provided by Bhola et al. [39], the dataset was segmented into three unique subsets: sixty percent was designated for training, twenty percent was designated for validation, and twenty percent was designated for testing. The hyperparameters of our model are going to be optimized through the use of fine-tuning, which is the purpose of the validation set. Securities are classified into 104 different categories according to Standard 3 of the Shenwan Industry Classification. The ‘fund-holding’ information had been taken from the quarterly reports of 61 A-share mutual funds that had been founded previous to the year 2013. Table 1 provides a comprehensive overview of the dataset's information in its entirety.

Table 1. Dataset summary

Baselines: The authors benchmark stock movement prediction findings against those of prior research, which includes five newly suggested graph neural network algorithms, one standard LSTM model, one multifaceted attention LSTM, and one trading strategy called mean reversion (MR).

1. MR: The model made use of the average reversion indicator in order to provide a prediction regarding the reversion of the local trend. The assumption that the price will revert to its previous position after experiencing significant volatility was the means by which this objective was fulfilled [39].
2. LSTM: To predict how share prices will go in the future, the model used the LSTM algorithm, as stated in study [39].
3. DARNN: In order to efficiently anticipate, the model proposed using a recurrent neural network with a dual stage attention [40]. This would allow for the selective utilization of relevant features.
4. GCN+LSTM: An LSTM network was fed embeddings of stocks by the model, which was then used to learn relationships between stocks [40]. The model used GCN to learn about these interactions.
5. HATS: According to study [40] research, the model made use of a hierarchical attention network in order to learn in an adaptive manner the significance of using various relation types for stock prediction.
6. TGC: an innovative temporal graph convolution was utilized in order to represent the temporal evolution simultaneously, and relational embeddings of stocks were utilized in order to make predictions [40].
7. STHGCN: A unique Spatio-Temporal Hypergraph Convolution Network was proposed by study [40] in 2020 with the purpose of learning the evolution of stock prices over the course of stock industry relations.
8. HGTAN: This study developed a novel hypergraph tri-attention network with the purpose of predicting the movement of stock prices. The network took into account information regarding both industry affiliation and fund-holding [40]. This exemplifies the condition of the art at the present time.

Parameters: The authors run the specified ensemble learning framework using CUDA 10.2 and PyTorch 1.10.2. The authors tested the model using data from the latest 5, 10, and 20 trading days because the authors in the study [41] note that data longevity affects model performance. The authors employed hyperparameters tuned using study by Zhang et al. [41] validation set to level the playing field: For the temporal attention mechanism, $d_k$ and $d v$ are both eight, and stock has a feature dimension of 16, with a batch size of 32. Hidden GRU unit number 32. For the loss function 3, the study recommended setting $\beta$ as $1_{e-2}$ with a maximum of 600 epochs and a dropout rate of 0.5. Our baseline models are configured like their public counterparts.

Evaluation: The authors utilized the following metrics to evaluate the suggested model's classification effectiveness: accuracy, precision, recall, and F1 score. The metrics are computed as follows:

$\begin{gathered} Accuracy=\frac{T P+T N}{T P+T N+F P+F N} \\  Precision=\frac{T P}{T P+F P} \\ Recall=\frac{T P}{T P+F N}\end{gathered}$

The symbols TP and TN are used to denote the classes that have been positively predicted and the classes that have been negatively predicted, respectively. The mistakenly predicted positive classes are denoted by the symbol FP, whereas the incorrectly anticipated negative classes are denoted by the symbol FN. To compute the metric in the macro-setting, the authors make use of the scikit-learn module. At the same time, the authors perform multi-label classification, which involves three different movement directions. As an illustration, the formula for determining precision may be as follows:

$Precision =\left(\frac{T P_r}{T P_r+F P_r}+\frac{T P_s}{T P_s+F P_s}+\frac{T P_f}{T P_f+F P_f}\right) * \frac{1}{3}$

The acronyms r, s, and f represent the terms increase, steady, and decline, respectively.

4.2 Effectiveness results on the real-world dataset

The number of models that accurately predict the movement of stock prices on real-world benchmark datasets is presented in Tables 2-4. The look-back window for these models is the most recent five, ten, and twenty trading days. In terms of precision, recall, and F1 score, the suggested model beats the second-best baseline by increments of 1.14 percent, 3.63 percent, and 2.45 percent for three different trade periods. According to study by Li et al. [42], the F1 value takes into account precision and recall measurements, which helps to improve the sensitivity and generalizability of performance evaluation models. When it comes to investing in stocks, getting a high recall means making the most of every opportunity to generate money and also high precision. Therefore, it can be concluded that the F1 score is the most significant of these four parameters. The Wilcoxon signed rank test, a non-parametric used when the requirements for the t-test for two paired samples are not satisfied test, demonstrates that our model outperforms where (p>=0.5) the most advanced HGTAN, particularly in situations when sophisticated triple attention spanning hyperedges and hypergraphs is not utilized. Furthermore, our model improves the F1 score by 7.34 percent. Both hypergraph convolution and GCN are used to collect data on the movement of stock prices at the group level and pairwise, as demonstrated above. With data from the most recent 20 and 5 trading days, our model outperforms the competition, and it reaches its highest level of accuracy within a span of ten days.

Table 2. Results from comparing baselines and the suggested model for classification using data from five trading days

Table 3. Results from comparing baselines and the suggested model for classification using data from ten trading days

Table 4. Results from comparing baselines and the suggested model for classification using data from twenty trading days

4.3 Investment simulation and profitability

From April 23, 2019, to May 9, 2019, which is ten trading days, the authors compare our model to competitors using the same forecasting window size as study [42]. The findings are presented in Table 4. The constant prediction accuracy of the model, which reaches its highest point in five days, is one of its most significant advantages.

In seven days, it reaches an accuracy of more than 70 per cent (all accuracies more significant than 70 per cent are highlighted). The most advanced model, HGTAN, takes three days, and the rest of the models, for the most part, only take one of the ten trading days. Over ten trading days, four important market indices—the Hushen 300, the Shenzheng Zongzhi, the Shangzheng 50, and the Zhongxiao 300—entered what is known as a “bear market,” as seen in Figure 4. The Hushen 300, comprised of the 300 equities with the highest market capitalization and the most liquidity, witnessed a precipitous drop from 4019 on April 23, 2019, to 3599.7 on May 9, 2019, which caused investors to get concerned. In Figure 4, it is demonstrated that dropping stocks are prevalent for seven consecutive days (April 23, April 25, April 26, April 29, May 6, May 8, and May 9). Furthermore, our technique consistently achieves more than 70 per cent accuracy (except one day), demonstrating its effectiveness compared to other models and its capacity to avert loss.

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Figure 4. Different movement of stocks

The authors analyze the profitability of multiple models from August 31, 2018 to October 31,2019, as presented in Table 4, according to the reference [42]. The cumulative return rate, called CR, is frequently used in profitability analysis (B14). The abbreviation SR refers to the Sharpe ratio, a quantitative measure that assesses the relationship between investment returns and associated risks.

$ Sharpe\,\, Ratio=\frac{E\left(R_s-R_f\right)}{\sigma_s}$

Within this particular framework, the symbols $E, R_s$, and $R_f$ represent the expected value, stock return, and risk-free rate, respectively. For instance, the interest rate on a one-year deposit in 2019 is $1.5 \%$. The standard deviation of the excess return on investments is also denoted by the symbol $\sigma_s$. Our approach is competitive in terms of risk management and has the maximum cumulative return rate at $22.33 \%$. In addition, its Sharpe ratio of 0.775 is the highest of any model the authors evaluated, indicating that it generates a greater profit under identical risk conditions. However, the main problem with the Sharpe ratio is that it can be accentuated by investments that don't have a normal distribution of returns.

4.4 Discussion and analysis

The authors evaluate the classification accuracy of the dataset by analyzing data from the past ten trading days. In Table 5, the authors evaluate the effectiveness of the second-best model, HGTAN, with that of our proposed framework and its components. This study demonstrates the enhancements made to each module, both on an individual basis and as a whole, through the implementation of our proposed architecture.

• GCN+GRU+TA+HGCN (Module A): An HGCN learns the ins and outs of the stock market and the relationships between different fund-holding groups. For the purpose of improving pairwise relations, GCN processes historical pricing features alongside industry data. An embedding is produced by a GRU network that has a TA, or temporal attention layer.
• GRU+TA+HGCN (Module B): One distinguishing characteristic of version B is the lack of use of GCN for paired relations.
• GRU+TA+HGCN+Adv (Module C): Unlike variant A, this variation does not use GCN for pairwise relations. As suggested by the study [42], it expands HGCN with adversarial training to increase generalization to manage stock characteristic stochasticity.
• GRU+TA (Module D): This component serves as the basis, and it only makes use of historical pricing information.
• GRU+TA+GCN+HGCN (Module E): This compares Module A and shows that GCN captures pairwise relations before RNN models.
• GCN + GRU + TA + Adv (Module F): This variation is in opposition to the suggested approach to verify HGCN's worth.

Table 5. An ablation study of proposed framework on dataset with 10 trading days as record

The proposed framework prevails all versions in recall and F1 score because all modules improve performance relative to the baseline (Module D). The framework significantly outperforms HGTAN in accuracy, recall, and F1 score. Section 4.3 further notes that the proposed framework performs well during market downturns. When comparing modules, A and B, GCN improves F1 value by 0.33% and all four metrics by 2.28%. It's wrong to disregard pairwise relations because we've evaluated group-level data. GCN outperforms RNNs in price fluctuation learning.  GCN will improve RNN model prediction by capturing industry-based stock volatility trends. Adversarial training with stock price stochasticity improves model resilience. Comparing modules B and C, C's accuracy, recall, and precision drop but F1 score increases. Hypergraph convolution enhances module D's accuracy by 2.31%, according to module B. Precision and F1 score can improve 2.17% and 1.02%. Comparing module F with the proposed framework demonstrates that hypergraphs are needed to predict stock prices using group-level data.