# Financial Distress Prediction of Chinese Listed Companies Using the Combination of Optimization Model and Convolutional Neural Network

Authors: Lin Zhu; Dawen Yan; Zhihua Zhang; Guotai Chi
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

In order to predict financial distress in 3424 Chinese listed companies, we incorporate a novel time windows optimization model into a convolutional neural network and use 576 financial/nonfinancial/macroindicators as the model input data. Our prediction accuracy can reach 94.5%, at least 2% higher than known classifiers (e.g., support vector machine, decision tree, logistic regression, neural network). In terms of AUC and the Kolmogorov–Smirnov statistic, our model also outperformed these classifiers. The introduction of the optimization model in our model can combine indicator information in different time windows, leading to the best prediction performance.


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## Body

## 1. Introduction

Prediction of financial distress is becoming a hot topic over the decades, due to its great significance to companies, banks, and even the economy of a country. Creditors, especially banks, are often forced to bear many losses that should have been borne by the troubled companies with evading debt through bankruptcy. In the stock market, the prediction of financial distress can be used for monitoring of the solvency of regulated companies, assessment of loan default risk and the pricing of bonds and credit derivatives, and other securities exposed to credit risk [1–3]. Financial distress forecasting has been widely regarded as a promising way to reduce financial losses. If financial distress can be predicted reliably, managers of listed companies can take remedial measures in time to avoid the deterioration, and investors can grasp the profitability of listed companies, adjust investment strategies, and reduce investment losses. As China is becoming one of the main markets for international investors, the financial distresses of Chinese listed companies have attracted more and more attention. In China’s stock market, if a listed company has suffered losses for two (or three) consecutive years, this company will be marked as an ST (∗ST) company, and the corresponding stock will be marked as an ST (∗ST) stock. The ST (∗ST) stock quotation within a trading day is limited to +5%/−5% for an ST stock, while 10% for a normal stock. At present, the ST and ∗ST in the Chinese stock market is a mark for judging whether listed companies are in financial distress [4–7]. In 2017, 69 Chinese listed companies were marked as ST or ∗ST stock.In addition to obvious financial indicators, nonfinancial indicators are widely used as predictors in the financial distress. Company audit, number of employees, environmental protection investment, number of shareholders, and executive compensation have been considered in bankruptcy, default prediction, and evaluation of company development [8–11]. Balasubramanian et al. [12] used 9 financial variables (retention ratio, net profit margin, return on equity, etc.) and 4 nonfinancial variables (promoter holdings, age of the company, institutional holdings, promoter holdings pledged) to develop a financial distress model for Indian listed companies through conditional logit regression. Yu et al. [13] used the age and educational background of the chairman and the registered capital of the company to conclude that these nonfinancial factors are possibly more important than financial factors. Wang and Li [14] used 34 financial ratios and 5 nonfinancial ratios to test the accuracy of predicting the probability of financial distress of Chinese listed companies and found that the equity concentration factor performed best. Different from the previous studies, we will explore four categories of nonfinancial indicators, the corporate governance indicators: ownership structures and board structure, credit information, and social responsibility to forecast financial distress risk by means of latest deep learning models.Company production and operation are always in a certain economic environment, so its financial health is inevitably affected by the macro-economy. The high ratio of public debt to GDP and the high unemployment rate are positively correlated with company failures. Pesaran and Hashem [15] found that macro factors (e.g., stock index, interest rate, inflation rate, oil price, and output gap) have a significant impact on the financial status of companies under the Morton credit risk model. Khoja et al. [16] found that the combination of financial and macroeconomic data plays a key role in cross-regional financial distress. So far, the combination of macroindicators and financial and nonfinancial indicators has been applied only in bankruptcy prediction. Jones [17] used financial indicators (net profit rate and annual growth rate of working capital), macroindicators (real GDP/real GDP growth, CPI index, interest rate level, public debt GDP, unemployment rate), and nonfinancial indicators (the impact of company age, company size, and audit type) to study American bankrupt companies. At present, there is no research on the combination of macroindicators with financial and nonfinancial indicators to predict financial distress.Different time windows have gradually become a mainstream method to forecast financial distress. Sun et al. [18] used a three-year time window (t−1, t−2, and t−3 year) separately to predict the ST of Chinese listed companies in year t by the AdaBoost integrated model. Geng et al. [19] used three single-year time windows (t−3, t–4, and t−5 year) to predict ST at year t and found that the forecast performance of the time windows year t-5 is better than that of the time window year t−3. Li et al. [20] used a three-year time window (t−1, t−2, t−3 years) to construct the outranking relations (OR)-case-based reasoning model for financial distress prediction. Yan et al. [21] introduced the 3–5 years lagging financial ratio and macroeconomic factors into the financial forecasting model. Wu [22] analysed 21 financial indicators information under a five-year time window in the financial crisis prediction by using traditional statistical models (Fisher linear decision analysis, multiple linear regression analysis, and logistic regression analysis). Since these traditional statistical models are severely limited by multicollinearity conditions, they have limited ability to extract information from potentially important variables and related interaction effects. However, Wu [22] did not consider nonfinancial and macroindicator information and did not integrate the forecast results of different years.Various advanced financial distress models have been well developed. Sun and Li [23] applied a combination of multiple classification models to predict financial distress in Chinese listed companies. The weighted majority voting combination model can have better prediction than a single model (e.g., neural networks, decision trees, and support machine vector models) [24, 25]. Geng et al. [19] compared neural networks with majority voting, decision tree, and support vector machine by using 31 financial indicators and indicated that the neural network’s performance is the best. Jiang & Jones [26] combined financial and nonfinancial indicators using the TreeNet to predict financial distress. Most of these models usually depend on the assumption of linear separability and multivariate normality between explanatory variables [27, 28]. When the independence between explanatory variables cannot be met, such an assumption adversely affects the prediction accuracy [29]. Deep learning models do not require high independence between variables [30, 31]. Hosaka [32] applied the GoogLeNet model to predict the bankruptcy of Japanese companies by using financial ratio data as input variables. Tang et al. [33] used deep neural networks (DNN), recurrent neural networks (RNN), and long short-term memory (LSTM) to find that text features played a more important role in supplementing the traditional financial features of Chinese listed companies’ financial distress predictions.In this study, we will use the combination of convolutional neural network and time windows optimization model to predict the financial distress of 3424 Chinese listed companies. The 576 financial/nonfinancial/macroindicators are used as predictor variables. The optimized use of 576 indicators in time windows will not only increase the predictive performance of convolutional neural networks but also make some interpretability of convolutional neural networks in financial scenarios. Our prediction accuracy can reach 94.5%, at least 2% higher than known classifiers (e.g., support vector machine, decision tree, logistic regression, neural network). In terms of accuracy, AUC, and the Kolmogorov–Smirnov statistic, our model outperformed these classifiers.


## 2. Classic Prediction Models

Financial distress prediction models have been developed with the help of various machine learning [34–37], and their performance depends on different country specificities, methods, and variables used to construct these models [38, 39].Artificial neural network (NN) is an extensive parallel interconnected network of neurons [40]. Neurons receive input signals from other neurons through weighted connections. The total input value received by the neuron is compared to the neuron’s threshold and then processed through an activation function to produce the neuron’s output. Geng et al. [19] used a neural network model to predict the financial distress of Chinese listed companies and indicated that the neural network’s performance is the best.Support vector machine (SVM) is linear classifier that can be used for classification and regression analysis [41] by finding the optimal hyperplane which can separate two different classes and maximum margin of separation. SVM can perform well with high-dimensional feature spaces since it aims to determine an optimum direction of discrimination in the feature space [42]. Since financial distress data are complex, high-dimensional data, SVMs are suitable tools to predict financial distress [43].The CART is one of the most widely used decision tree models for classification [44]. CART can determine the attribute of the samples by selecting the gain ratio as the criterion for splitting samples into subsets at each node. Thanks to its pruning mechanism, CART overcomes overfitting and eliminates the exceptions and noise in the training set [42].Logistic regression (LR) is a binomial regression model in the family of generalized linear models [45, 46]. In LR, the probability of some event happening is modelled as a linear function of a set of predictor variables [47]. Similar to SVM, LR is also a linear classifier and can yield promising results to predict financial distress.Convolutional neural network [48] consists of three parts: convolutional layer, pooling layer, and fully connected layer. The convolutional layer denoises, the pooling layer extracts features, and the fully connected layer functions as a classifier. The learning CNN parameters are performed by using the training datasets. Although the higher-level CNNs show high recognition performance due to the continuous fully connected layers, the large number of parameters possibly makes the learning process very inefficient [49]. Although the CNN has been successfully applied to image and speech recognition [50–53], there are only a few applications of a CNN to financial fields: Ding et al. [54] used the CNN to predict a share price; Hosaka [32] used the CNN to predict the bankruptcy of Japanese companies in 2019.


### 2.1. Data

We will predict financial distress in 3424 companies listed on Shanghai and Shenzhen stock exchanges. Based on the China Securities Regulatory Commission classification (GB/4754-2011), these companies are divided into 18 industry categories (Tables1 and 2). In China’s stock market, if a listed company has suffered losses for two (or three) consecutive years, this company will be marked as an ST (∗ST) company, and the corresponding stock will be marked as an ST (∗ST) stock. The distribution of financial distress companies (ST or ∗ST) in different years is shown in Table 3. At present, the ST and ∗ST in the Chinese stock market is a basis for judging whether listed companies are in financial distress [4–7].Table 1
Classification of Chinese listed companies.
Code standardClassificationTotal number in 2017AAgriculture, forestry, animal husbandry, and fishery44BMining industry75CManufacturing industry2173DElectricity, heat, gas and water production, and supply industry104EConstruction industry99FTransportation, warehousing, and postal services93GInformation transmission, software, and information technology service industry244HWholesale and retail businesses162IAccommodation and catering services industry9JFinancial industry77KThe real estate industry124LLeasing and business services industry46MScientific research and technology service industry40NWater conservancy, environment, and public facilities management industry42PEducation industry3QHealth and social work industry9RCulture, sports, and entertainment industry57SComprehensive industry23Table 2
Number of financially distressed companies during 2012–2017.
Industries201220132014201520162017A323222B511156C562929373843D820320E433001F132100G950114H202253I100102J220020K541245L101000M000010N110201P000001Q000010R411010S310021Total1055443526469Table 3
The overall distribution of listed companies in China from 2012 to 2017.
YearsSTNon-STST proportion (%)201210532393.1420135433701.5820144333811.2620155233721.5220166433591.8720176933552.02We collect the 576 financial/nonfinancial/macroindicators of 3424 listed companies from the wind database (https://www.wind.com.cn), the CSMAR database (https://www.gtarsc.com), and the RESSET database (https://www.resset.cn) (Table 4). Among 576 financial/nonfinancial/macroindicators, 333 financial indicators are divided into solvency, profitability, operation ability, and growth ability; 108 nonfinancial indicators are divided into the internal structure, senior management, credit, and societal responsibility; 135 macroindicators are divided into national income, employment, national consumption, investment costs, societal factors, and ecological factors.Table 4
Financial distress forecast indicators.
TypesNumbersIndicatorsPropertyTypesNumbersIndicatorsPropertyFinancial indicatorsSolvency1Debt to asset ratioNegativeOperation ability224Current assets/total assetsPositive2Current ratioPositive225Operating cycleNegative..................87Acid-test ratioPositive282Total assets turnoverNegativeProfitability88Total operating income per sharePositiveGrowth ability283Net assets per sharePositive89Ratio of sales to costNegative284Total assetsPositive..................223Net profit margin on salesPositive333Increase rate of main business revenuePositiveNonfinancial indicatorsCorporate governance334Whether financial institutionQualitativeCredit information409Whether the third party inspectionQualitative335Preaudit situationQualitative410Whether the largest shareholder has changedQualitative..................400Total employeesPositive438Whether illegalQualitativeBoard structure401Chairman’s genderQualitativeSocietal responsibility439Total taxPositive402Chairman’s ageQualitative440Social contribution value per sharePositive.........441Social donationPositive408Chairman’s degreeQualitativeMacroindicatorsNational income442Regional GDPPositiveSocietal factors516Natural population growth ratePositive443M1 money supplyPositive517Number of domestic patent applications grantedPositive..................462Industry indexPositive532Total education expenditurePositiveEmployment463Employee remunerationPositiveInvestment costs533Short-term benchmark interest rateNegative464Number of employeesPositive534Long-term benchmark interest rateNegative..................477Unemployment rateNegative568Total foreign investmentPositiveNational consumption478Engel’s coefficientNegativeEcological factors569Water resources per capitaPositive479Final consumption expenditurePositive570Garbage treatment ratePositive..................515Total social retailPositive576Electricity consumptionPositiveIn order to eliminate the influence of the unit and dimension of quantitative indicators, the 0–1 standardized method will be applied to all positive/negative quantitative indicators. For the positive quantitative indicator, the larger its value, the better the financial status of the listed company. For the negative quantitative indicator, the smaller its value, the better the financial status of the listed company. As each quantitative indicator is measured on a different scale, these indicators are standardized as follows:(i)
X=V−Vmin/Vmax−Vmin for positive indicator V(ii)
X=Vmax−V/Vmax−Vmin for negative indicator VThe above standardization process is to map all quantitative indicators into [0, 1].All qualitative indicators are standardized by using the followingWeight of Evidence：(1)WOE=lnm0/M0m1/M1=lnm0/m1M0/M1,where m0 and m1 are the number of financial health and distress companies under the characteristic of the qualitative indicator, M0 and M1 are the total number of healthy and distress companies, respectively. Similar to quantitative indicators, WOE will be further linearly mapped to [0, 1].


## 2.1. Data

We will predict financial distress in 3424 companies listed on Shanghai and Shenzhen stock exchanges. Based on the China Securities Regulatory Commission classification (GB/4754-2011), these companies are divided into 18 industry categories (Tables1 and 2). In China’s stock market, if a listed company has suffered losses for two (or three) consecutive years, this company will be marked as an ST (∗ST) company, and the corresponding stock will be marked as an ST (∗ST) stock. The distribution of financial distress companies (ST or ∗ST) in different years is shown in Table 3. At present, the ST and ∗ST in the Chinese stock market is a basis for judging whether listed companies are in financial distress [4–7].Table 1
Classification of Chinese listed companies.
Code standardClassificationTotal number in 2017AAgriculture, forestry, animal husbandry, and fishery44BMining industry75CManufacturing industry2173DElectricity, heat, gas and water production, and supply industry104EConstruction industry99FTransportation, warehousing, and postal services93GInformation transmission, software, and information technology service industry244HWholesale and retail businesses162IAccommodation and catering services industry9JFinancial industry77KThe real estate industry124LLeasing and business services industry46MScientific research and technology service industry40NWater conservancy, environment, and public facilities management industry42PEducation industry3QHealth and social work industry9RCulture, sports, and entertainment industry57SComprehensive industry23Table 2
Number of financially distressed companies during 2012–2017.
Industries201220132014201520162017A323222B511156C562929373843D820320E433001F132100G950114H202253I100102J220020K541245L101000M000010N110201P000001Q000010R411010S310021Total1055443526469Table 3
The overall distribution of listed companies in China from 2012 to 2017.
YearsSTNon-STST proportion (%)201210532393.1420135433701.5820144333811.2620155233721.5220166433591.8720176933552.02We collect the 576 financial/nonfinancial/macroindicators of 3424 listed companies from the wind database (https://www.wind.com.cn), the CSMAR database (https://www.gtarsc.com), and the RESSET database (https://www.resset.cn) (Table 4). Among 576 financial/nonfinancial/macroindicators, 333 financial indicators are divided into solvency, profitability, operation ability, and growth ability; 108 nonfinancial indicators are divided into the internal structure, senior management, credit, and societal responsibility; 135 macroindicators are divided into national income, employment, national consumption, investment costs, societal factors, and ecological factors.Table 4
Financial distress forecast indicators.
TypesNumbersIndicatorsPropertyTypesNumbersIndicatorsPropertyFinancial indicatorsSolvency1Debt to asset ratioNegativeOperation ability224Current assets/total assetsPositive2Current ratioPositive225Operating cycleNegative..................87Acid-test ratioPositive282Total assets turnoverNegativeProfitability88Total operating income per sharePositiveGrowth ability283Net assets per sharePositive89Ratio of sales to costNegative284Total assetsPositive..................223Net profit margin on salesPositive333Increase rate of main business revenuePositiveNonfinancial indicatorsCorporate governance334Whether financial institutionQualitativeCredit information409Whether the third party inspectionQualitative335Preaudit situationQualitative410Whether the largest shareholder has changedQualitative..................400Total employeesPositive438Whether illegalQualitativeBoard structure401Chairman’s genderQualitativeSocietal responsibility439Total taxPositive402Chairman’s ageQualitative440Social contribution value per sharePositive.........441Social donationPositive408Chairman’s degreeQualitativeMacroindicatorsNational income442Regional GDPPositiveSocietal factors516Natural population growth ratePositive443M1 money supplyPositive517Number of domestic patent applications grantedPositive..................462Industry indexPositive532Total education expenditurePositiveEmployment463Employee remunerationPositiveInvestment costs533Short-term benchmark interest rateNegative464Number of employeesPositive534Long-term benchmark interest rateNegative..................477Unemployment rateNegative568Total foreign investmentPositiveNational consumption478Engel’s coefficientNegativeEcological factors569Water resources per capitaPositive479Final consumption expenditurePositive570Garbage treatment ratePositive..................515Total social retailPositive576Electricity consumptionPositiveIn order to eliminate the influence of the unit and dimension of quantitative indicators, the 0–1 standardized method will be applied to all positive/negative quantitative indicators. For the positive quantitative indicator, the larger its value, the better the financial status of the listed company. For the negative quantitative indicator, the smaller its value, the better the financial status of the listed company. As each quantitative indicator is measured on a different scale, these indicators are standardized as follows:(i)
X=V−Vmin/Vmax−Vmin for positive indicator V(ii)
X=Vmax−V/Vmax−Vmin for negative indicator VThe above standardization process is to map all quantitative indicators into [0, 1].All qualitative indicators are standardized by using the followingWeight of Evidence：(1)WOE=lnm0/M0m1/M1=lnm0/m1M0/M1,where m0 and m1 are the number of financial health and distress companies under the characteristic of the qualitative indicator, M0 and M1 are the total number of healthy and distress companies, respectively. Similar to quantitative indicators, WOE will be further linearly mapped to [0, 1].


## 3. Methods

Ensemble learning [38] is a promising research direction in machine learning research [55, 56]. Inspired by ensemble learning, in this study, we will use the combination of convolutional neural network and time windows optimization model to predict the financial distress of 3424 Chinese listed companies.Due to the fact that the CNN is more effective for image processing, we will first use the “minimum energy” method to convert 576 financial/nonfinancial/macroindicators into images, where adjacent pixel positions are assigned to highly correlated indicators instead of randomly placed [32]. The energy of the matrix is defined as follows:(2)E=∑j1,j2∈PcovRj1,Rj2dj1,j2,where d (j1, j2) is the Euclidean distance between indicators j1 and j2, and R (j1) and R (j2) are the value vector of indicators j1 and j2. Initially, 576 robust indicators were transformed into a 24∗24 matrix randomly, and the corresponding energy is called the initial energy. We minimize the energy in (1) by exchanging indicator positions in pairs. An example of initial energy and minimal energy indicators of a financial distress ST company is shown in Figure 1.Figure 1
Express indicators of a financial distress company as a grey image with (a) initial energy and (b) minimum energy.
(a)(b)We first use CNN to predict the probability of financial distress. We divide 3424 companies into the training set, validation set, and test set at a ratio of approximately 6 : 1:1; that is, there are 2515 training samples, 420 verification samples, and 420 test samples. It can be observed that the number of non-ST companies is much larger than ST companies (Table3), and such a high imbalance will affect the prediction accuracy significantly [57]. In order to solve it, we used the known Synthetic Minority Oversampling Technique (SMOTE) [58] to expand the number of ST (∗ST) companies such that the ratio of ST and non-ST is close to 1 : 1. Unlike simply repeated sampling, the SMOTE method artificially synthesizes new samples based on minority samples to reduce the problem of model overfitting [57]. The SMOTE algorithm is as follows.Step 1.
For each samplex in the ST (∗ST) class, calculate the Euclidean distance from it to the others in the ST(∗ST) class sample set, and get its k-nearest neighbours.Step 2.
Randomly select several samplesx1, x2, …, xn from its k-nearest neighbours of the sample x.Step 3.
Construct a new samplexnew with the original sample x:(3)xnew=x+rand0,1▱xi−x,where rand (0, 1) represents a random number in (0, 1).
All indicators int − 1, t − 2, t − 3, t − 4, and t − 5 years are input, respectively, into the convolutional neural network. The output is the probability that financial distress occurs in year t, denoted by pt − 1, pt − 2, pt − 3, pt − 4, pt − 5. Due to the limited information available in a single year, if more years are used, a better prediction can be expected. Therefore, we develop a novel optimal model to search for the optimal weight of time windows for the financial distress prediction. By using the validation set and the optimization model (3–4), we optimize the predicted probability to make it closer to the real probability of financial distress occurring Yt.(4)minw1,w2,w3,w4,w5∑q=15wqpt−q−Yt2+∑q=15wq1−pt−q−1−Yt2,s.t.0<wq<1,∑q=15wq=1,q=1,2,3,4,5.
For the output probability of financial distress, when it exceeds 0.5, the company is judged as an ST company in yeart; otherwise, it is judged as a non-ST company. The whole schematic diagram of our financial distress model is shown in Figure 2. Our model can take good advantage of the high prediction accuracy of deep learning and the powerful optimization capability of the optimization model.
To evaluate the performance of prediction models, prediction accuracy, area under curve, and Kolmogorov–Smirnov (KS) are used in this study.
Prediction accuracy is one of the most widely used measures for the evaluation of prediction models, and it is defined as follows:(5)accuracy=TN+TPTP+FP+FN+TN,where TN, TP, FP, and FN denote the number of true negatives, true positives, false positives, and false negatives, respectively.
Area under curve (AUC) is the area under the receiver-operating characteristic (ROC) curve. The ROC curve is obtained by varying the threshold for the predictive probability or the discriminant function. AUC takes on values from 0 to 1. The higher values of AUC indicate better performance of the prediction models.
Kolmogorov–Smirnov (KS) refers to evaluating the discriminative ability of the model by measuring the difference between the cumulative distribution of good and bad samples. The larger the KS value, the better the discrimination between good and bad samples.Figure 2
Schematic diagram of our financial distress model.


## 4. Results and Discussion

We will predict financial distress in 3424 companies listed on Shanghai and Shenzhen stock exchanges by using our combined model. We will compare our model with known neural network (NN), support vector machine (SVM), decision tree (CART), and logistic regression (LR) models. To evaluate the predictive performance of our models, prediction accuracy (accuracy), area under the curve (AUC), and Kolmogorov–Smirnov (KS) were used as the evaluation metrics.First, we consider using the time window 2012–2016 to predict financial distress in 2017. The prediction performance of our model and pure CNN is shown in Table5, and the optimal prediction weights of time windows in the optimization model are shown in Table 6. The largest weight is assigned to the time window 2016, and the introduction of the optimization model will enhance the prediction accuracy by 13.45%. Second, we consider using the time window 2012–2015 to forecast financial distress in 2017. The corresponding prediction is shown in Tables 7 and 8. The largest weight is assigned to time widow 2015, and the introduction of the optimization model will enhance the prediction accuracy by 2.28%. From both cases, it is clear that the introduction of our optimization model can improve the prediction accuracy of pure CNN. As we all know, because pure CNN is like a black box, it may treat 2016 information as redundant information. As a result, the time window 2012–2016 is inferior to the time window 2012–2015 when making predictions. However, when CNN is combined with the optimization model, it successfully reflects the information value of 2016, making the prediction performance of the time window 2012–2016 better than the time window 2012–2015. This reflects precisely that when convolutional neural networks are combined with external optimization models, financial distress forecasts can be better improved.Table 5
The prediction performance with/without optimization of CNN for time window 2012–2016.
ModelsAccuracy (%)AUCKSPure CNN81.050.62110.6193CNN + optimization model94.500.99740.9857Table 6
The weights of optimization forecast model for time window 2012–2016.
Years20162015201420132012Weights0.380410.32620.19590.01890.0785Table 7
The prediction performance with/without optimization of CNN for time window 2012–2015.
ModelsAccuracy (%)AUCKSPure CNN86.240.92540.6338CNN + optimization model88.520.95480.7774Table 8
Optimal weights of combination optimization forecast model from 2012 to 2015.
Years2015201420132012Weights0.85650.143500In terms of accuracy, KS, and AUS, we compare our model with known NN, SVM, CART, and LR models under time windows (Table9). In order to compare fairly the logistic regression model with our model, we delete collinearity indicators before training the logistic regression model. For the case of single-year time windows, the highest prediction accuracy predicted by NN, CART, SVM, and LR model is 85.52% (2015), 83.05% (2016), 91.09% (2016), and 88.92% (2016), respectively. In the case of the multiyear time window, our model has the highest prediction accuracy of 88.52% (2012–2015) and 94.5% (2012–2016), followed by SVM with prediction accuracy of 86.90% (2012–2015) and 92.37% (2012–2016) and NN with prediction accuracy of 72.98% (2012–2015) and 92.66% (2012–2016). In summary, the prediction performance of our model is better than other models. The combination of CNN and the optimization model in our model can take good advantage of the high prediction accuracy of deep learning and the powerful optimization capability of the optimization model.Table 9
Prediction results of different models.
YearsCriterionNNCARTSVMLROurs2012–2016Accuracy92.66%80.39%92.37%88.59%94.5%KS0.81640.59870.80870.7380.9857AUC0.85770.61260.85170.77860.99742012–2015Accuracy72.98%54.38%86.90%85.10%88.52%KS0.37710.50840.64150.60250.7774AUC0.5130.29080.75390.72340.95482016Accuracy83.05%82.15%91.09%88.92%N/AKS0.57690.62660.76890.7224N/AAUC0.68560.65210.82860.7881N/A2015Accuracy85.52%77.92%84.09%86.38%N/AKS0.59060.54010.60160.6526N/AAUC0.7310.5690.70250.743N/A2014Accuracy68.82%70.17%76.12%73.54%N/AKS0.34510.3870.29830.2884N/AAUC0.46580.43520.57930.5383N/A2013Accuracy76.38%76.12%79.42%71.48%N/AKS0.38270.46030.38980.2662N/AAUC0.57890.56050.63060.508N/A2012Accuracy72.46%71.67%72.19%64.71%N/AKS0.33460.38810.30250.3435N/AAUC0.51960.47990.52010.4175N/AFinally, we consider using a few significant indicators to demonstrate the performance of our model. We use logistic regression with lasso penalty [59, 60] to select 58 significant indicators from 576 indicators. After indicator selection, our model prediction performance is still the best, and its prediction accuracy is reduced slightly from 94.5% to 89.95% (Tables 9, 10).Table 10
Prediction results of different models with indicator selection.
YearsCriterionNNCARTSVMLRCNNOurs2012–2016Accuracy83.85%81.94%75.36%70.93%83.25%85.53%KS0.82780.63700.46650.57460.90700.9068AUC0.97840.99760.97830.99210.97770.97832012–2015Accuracy57.06%58.37%75.48%56.82%80.14%85.17%KS0.21170.78870.50720.85340.80160.9021AUC0.69730.97830.99760.99150.98150.9766Variable selection slightly improves the prediction performance of a few models and significantly decreases the prediction performance of the rest models. Therefore, the use of more indicators has gradually become a trend in financial forecasting. The more indicators contain information for better prediction, and the less information will reduce the forecast accuracy.


## 5. Conclusions

As China is becoming one of the main markets for international investors, the financial distresses of Chinese listed companies have attracted more and more attention. The combination of macroindicators and financial/nonfinancial indicators has not been applied to predict such financial distress. This study is the first to use 576 financial, nonfinancial, and macrofactors in time windows to predict financial distress in 3424 Chinese listed companies. In order to obtain a better accurate prediction, we establish an optimization model to search the optimal weight for time windows and combine it with a CNN model. Compared with pure CNN, our model can give some interpretability in impacts of different-year indicator information on financial distress. Experimental results showed that our model is superior to the representative traditional methods, such as CART, SVM, LR, NN, and CNN. In the future, our optimization model can be expected to apply to the optimization of the outputs of other deep learning models, especially in the involvement of heterogeneity at different times.



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