The design of early warning software systems for financial crises in high-tech businesses using fusion models in the context of sustainable economic growth

Logistic regression model

Regularization parameter learning

The learning curve adjusts the regularization parameters. The results are shown in Fig. 1.

As shown in Fig. 1, with the increasing of regularization parameter c, the intensity of regularization becomes smaller, whose performance is getting better and better in both the training set and test set. Until about 0.12, the performance on the training set still showed an upward trend. Too big a step can cause a jolt in the learning curve, but the performance on the unknown data set began to decline. The model has the problem of over-fitting, so it can be assumed that c is better set to 1.2.

XGboost model

Parameter optimization

Optimizing the model’s parameters is necessary to improve the generalization ability of the XGboost model on unknown data sets. In the XGboost model, there are three kinds of super parameters: general parameters, booster parameters and learning objective parameters, which are used to control the fitting data ability of the model. Booster parameters are mainly used to control the iterative process of each base decision tree, including maximum depth, learning rate, and minimum cotyledon sample weight. The interaction of many parameters may reduce the training time and accuracy of the model. In careful consideration of the data set used in this article, eight of the parameters adjusted in this empirical study are involved. In the actual training, we will first make a baseline demo to explore the model’s potential as quickly as possible so we can focus on integrating features and the model in the later period. Therefore, only eight parameters are set. Learning objective parameters control the ideal optimization objectives in each iteration process. The research in this article belongs to a two categories problem and needs to predict the probability of a financial crisis of HTE in unknown data sets. Therefore, the objective (minimum loss function) parameter is binary: logistic. The results are shown in Fig. 2.

It can be seen from the curve that the original XGboost model is in the state of overfitting, so it is decided to optimize it to make the results of the training set and the test set as close as possible. Suppose the effects on the test set cannot be increased. In that case, it is also an excellent choice to reduce the results on the training set, that is, to make the model not completely dependent on the training data and increase the model’s generalization ability. To describe the pruning process more clearly, this article uses three groups of curves to compare: one group is used to show the results of the original model data, one group is used to show the results of the previous parameter adjustment, and the last group is used to show the results of the parameters of the model is adjusted. Table 1 shows the optimal values of the eight parameters of the final model.

Table 1:

Parameter setting of XGboost model.

Parameter label	Meaning of parameters	Optimal value
eta	Learning efficiency	0.06
max_depth	Maximum depth of decision tree	2
gamma	Regular term parameters	0.3
lambda	Regular term parameters	0.3
alpha	Regular term parameters	0.3
colsample_bynode	Node subsampling rate	0.8
colsample_bylevel	Depth subsampling rate	1
colsample_bytree	The proportion of characteristic number in random sampling	0.8

DOI: 10.7717/peerj-cs.1326/table-1

BP neural network

It contains seven input nodes and five hidden layer nodes. As long as the network error reaches 0.00001 or the number of iterations reaches 1,000, the network will automatically stop training output. A 7 × 5 × 1 BP neural network topology structure is constructed. The training results are shown in Fig. 3.

The BP neural network training results in Fig. 3 show that the neural network’s training stops after 284 training times. With the continuous decline of MSE, the training error decreases to 9.9205 * 10⁻⁶ after 284 training times, less than the target error of 0.00001, and the training meets the requirements. The fitting coefficient of sample R is 0.99998, which shows that the fitting effect is perfect. Generally speaking, if the R-value is above 0.9, the fitting effect of BP network training can achieve the expected goal.

Index selection

This article takes the enterprises identified as HTE in China’s A-share market as the research object. It takes “Special Processing (ST)” as the standard to divide normal financial and financial crisis enterprises. A total of 462 HTE from 2018 to 2020 are selected as empirical samples, of which 42 are ST enterprises and 420 are nonST enterprises. The ratio of the two kinds of samples is 1:10, which has a serious imbalance. The experiment is divided into a training set and a test set by a five-fold cross-validation method, with “−1” for normal financial enterprises and “+1” for financial crisis enterprises.

Combined with the characteristics of high and new technology enterprises, such as significant intangible assets and strong research and development ability, the financial crisis of high and new technology enterprises is judged from many aspects. By referring to the existing research (Du, 2021), this article initially selects 30 financial indicators of the enterprise as the alternative indicators. Before the experiment, 13 indicators with missing data were eliminated, and 17 were retained as the model’s input variables. The sample indicators are shown in Table 2.

The data in this article are from the Guotai’an financial database, and the financial index data of the sample enterprises in the 2 years before the financial crisis (T-2) are selected as the experimental input. Before the empirical analysis, the data is normalized to obtain new financial index data ${\mathrm{x}}_{\mathrm{i}}^{\ast },\mathrm{i}=1,2,\cdots ,17$.

Evaluation method

The model’s prediction accuracy is a mainstream evaluation index in the existing research. If the accuracy rate is higher, the model has better warning performance. Predicted results usually contain the correct sample $\left|\mathrm{T}\right|$ and error sample $\left|\mathrm{F}\right|$. The prediction of Accuracy A is calculated as follows:

$$\mathrm{A}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{y}={\displaystyle \frac{\left|\mathrm{T}\right|}{\left|\mathrm{T}\right|+\left|\mathrm{F}\right|}}$$

With a class of non-equilibrium samples, it is not scientific and effective to use the prediction accuracy as the evaluation index of the model because the prediction results tend to incline to the majority of samples, and it is easy to ignore a small number of samples, leading to uneven prediction results. Therefore, this article also introduces the geometric mean accuracy rate G (g-mean) and F (F1_score) as evaluation indexes to evaluate the performance of the FCEW of HTE. The construction process of the three evaluation indicators is as follows:

Assuming that $\left|\mathrm{F}{\mathrm{S}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\right|$ and $\left|\mathrm{F}{\mathrm{S}}_{\mathrm{m}\mathrm{a}\mathrm{j}}\right|$ made of ST companies sample differentiating respectively divided into ST sample enterprise and the ST enterprises made samples of differentiating into non-ST the number of samples. $\left|\mathrm{T}{\mathrm{S}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\right|$ and $\left|\mathrm{T}{\mathrm{S}}_{\mathrm{m}\mathrm{a}\mathrm{j}}\right|$ of the ST and the ST enterprises, the number of samples correctly, usually expressed using a confusion matrix, as shown in Table 3.

Using the matrix, we can divide the four situations in the experiment. Then we can get the Response rate RE, the Specificity S and the Precision P through the relevant calculation:

(10) $$\mathrm{R}\mathrm{E}={\displaystyle \frac{\left|\mathrm{T}{\mathrm{S}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\right|}{\left|\mathrm{T}{\mathrm{S}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\right|+\left|\mathrm{F}{\mathrm{S}}_{\mathrm{m}\mathrm{a}\mathrm{j}}\right|}}$$

(11) $$\mathrm{S}\mathrm{P}={\displaystyle \frac{\left|\mathrm{T}{\mathrm{S}}_{\mathrm{m}\mathrm{a}\mathrm{j}}\right|}{\left|\mathrm{T}{\mathrm{S}}_{\mathrm{m}\mathrm{a}\mathrm{j}}\right|+\left|\mathrm{F}{\mathrm{S}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\right|}}$$

(12) $$\mathrm{P}={\displaystyle \frac{\left|\mathrm{T}{\mathrm{S}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\right|}{\left|\mathrm{T}{\mathrm{S}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\right|+\left|\mathrm{F}{\mathrm{S}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\right|}}$$

Then, $\mathrm{G}$ and $\mathrm{F}$ can be calculated as follows:

(13) $$\mathrm{G}=\sqrt{\mathrm{R}\mathrm{E}\times \mathrm{S}\mathrm{P}}$$

(14) $$\mathrm{F}={\displaystyle \frac{2\times \mathrm{R}\mathrm{E}\times \mathrm{P}}{\mathrm{R}\mathrm{E}+\mathrm{P}}}$$

Among them, G comprehensively investigates the model’s prediction performance for two kinds of samples with high reference values when the data is unbalanced. If G is large, the model’s accuracy is high, and vice versa. However, F mainly investigates the model’s prediction performance for several samples. If F is more significant, it indicates that the model performs better in predicting financial crisis samples and vice versa.

The area under the ROC curve (AUC) is introduced to quantitatively evaluate the classifier’s performance. AUC measures the probability of placing positive samples ahead of negative examples, regardless of the domain value. The larger the area of AUC, the better the classification effect.

Results and discussion

The boosting algorithm, where the learner is associated with Boosting, the latter one needs to learn from the previous one. Stacking is the result of a greater generalization in integrated learning. Stacking results from the aggregation method’s generalization in ensemble learning, which belongs to a hierarchical framework. Suppose a two-layer stacking model input the initial training set in the first stage, let multiple base learners learn and fit, and takes the output results as the input of the second stage classifier (meta leamer) for retraining. The final prediction result is obtained. The feature of this model is that it uses the prediction of the first stage as the feature of the prediction of the next level. In this article, two common model fusion methods, voting and averaging, are used to compare, respectively. The stacking method is an automated, large-scale integration policy. Overfitting can be effectively combated by adding regularization terms, and it does not require too much parameter tuning and feature selection. It is helpful for comparison and experimentation in this study.

Because the XGboost model did well in the previous research and was more stable, the prediction results of the three basic models are used as the characteristic variables that are substituted into the XGboost model to train it.

Any two of the three base models are fused. Among them, the fusion model of logistic regression and XGboost is named “model A,” the fusion model of XGboost and BP is named “model B,” and the fusion model of logistic regression and BP’s neural network model is called “model C”. The stacking fusion, voting, and averaging method fuse three single models: fusion model D.

The final three single models are compared and analyzed, and the results of each model on the test set are shown in Table 4.

Compared with the three single models, the accuracy of XGboost and logistic regression is about 83%, which is better than BP and even the Optimized BP neural network model. It can be seen that the recall rate of XGboost reaches 80%, which is equal to the optimized BP neural network model, and better than logistic regression model and BP neural network model. Next, the accuracy rate is still better with XGboost and logistic regression, in addition. Compared with each model’s AUC value, the XGboost model’s AUC value is 0.84, which is slightly better than the others. Even the optimized BP neural network model is only about 0.80.

Compared with the fused model, when the two single models are fused, the performance of models A, B, and C of the stacking fusion method is better than that of the other two fusion methods, which is more robust while maintaining a higher recall rate. The fusion effect of the voting fusion method is better when two single models are fused. In addition, through the comparison, we can see that the performance of stacking fusion method fusion model B is better than the other two models using the stacking fusion method in all aspects, which shows that the performance of a single model is better. When the performance of a single fusion model is closer, the performance of stacking fusion is better.

In addition, the accuracy of the stacking fusion model is 86.42%, which is slightly better than the voting fusion model and averaging fusion model; The accuracy of the three is close, but in the F that we are more concerned about, the stacking fusion model reaches 92.9%, that is to say, in the financial crisis enterprises given by the test set, more enterprises can be predicted more accurately, which is conducive to our research; At the same time, the AUC value of stacking fusion model is 0.887, which is better than other two fusion models.

The ROC curve of three single models is shown in Fig. 4.

It can be seen that the performance of the stacking fusion model on the test set is better, and the accuracy and AUC of the model are relatively higher while ensuring the recall rate. The ROC curve of the stacking fusion model fully covers the ROC curves of the other two fusion models, which indicates that the model constructed by the stacking fusion model has better performance than those built by the two model fusion methods of Voting and Averaging in this article. In addition, we can see that when the threshold is relatively low, the model performance fused by the Averaging model fusion method is similar to that of the stacking fusion model. However, as the threshold increases, the performance of the Averaging model fusion method is gradually worse than that of the other two model fusion methods.