1. bookAHEAD OF PRINT
Détails du magazine
License
Format
Magazine
eISSN
2444-8656
Première parution
01 Jan 2016
Périodicité
2 fois par an
Langues
Anglais
Accès libre

Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis

Publié en ligne: 15 Jul 2022
Volume & Edition: AHEAD OF PRINT
Pages: -
Reçu: 27 Jan 2022
Accepté: 23 Mar 2022
Détails du magazine
License
Format
Magazine
eISSN
2444-8656
Première parution
01 Jan 2016
Périodicité
2 fois par an
Langues
Anglais
Abstract

This article first uses a new method of nonlinear combination forecasting based on neural networks to construct a financial crisis early warning model and conduct an empirical study. The drafting article uses Fisher's second-class linear discriminant analysis and binary logistic regression to establish a three-year early warning model for listed companies before the financial crisis. Empirical research shows that this early warning model applies to various industries. It can play a certain role in predicting and preventing the financial crisis of Chinese companies.

Keywords

MSC 2010

Introduction

The multivariate model uses multiple financial indicators as the sample variables for the study. Combine multiple variables (indicators) to build a multivariate predictive analysis model. The statistical methods used in financial crisis early warning mainly include: multiple linear discrimination, multiple logistic regression, multiple probability ratio regression methods, etc. The multiple linear discriminant model (MDA) is mostly used from the research literature at home and abroad. Because its model is relatively simple, it is widely used, and the multivariate models established from that place mainly include Fisher's linear judgment model.

The actual situation and foreign research show different industries make the financial indicators and parameters included in the early warning financial crisis model different, so different models should be used for research and analysis [1]. Therefore, the empirical analysis of the multivariate model is carried out for the listed companies in the home appliance industry in China using multivariate statistical analysis methods. This can improve the pertinence, practicability, and operability of the model. First, according to the 28 financial indicators we selected and using cluster analysis, we will make a scientific, statistical classification of listed companies in the home appliance industry in China. Finally, the principal component analysis method is used to extract the principal components to calculate each component's scores and total scores. Sort the samples according to the total scores of the principal components to discover their financial crisis.

Selection of research samples and variables

The article takes 30 home appliance companies in China's listed companies as the research objects. At the same time, we use its financial data in 2021, 2020, and 2019 as the basis for analysis. This financial information all comes from its periodic public reports [2]. According to the characteristics of listed companies in China, we select net sales margin, main business profit margin, return on net assets, net asset interest rate, earnings per share (EPS), accounts receivable turnover rate, inventory turnover rate, total asset turnover rate, Working capital total assets ratio, debt-to-asset ratio, current ratio, quick ratio, equity ratio (debt-to-equity ratio), multiple of interest earned, the growth rate of main business income, the growth rate of net profit, the growth rate of net assets (increased equity Ratio), total asset growth rate, capital preservation and appreciation ratio, total cash-to-debt ratio (debt protection ratio), cash flow-to-debt ratio, cash inflow and outflow ratio, cash-to-sales ratio, profit quality index (operating index), net operating cash per share Flow, the cash recovery rate of all assets, retained earnings total assets ratio, net assets per share to establish an index system as analysis variables. These 28 indicators comprehensively reflect the company's profitability, solvency, asset management ability, growth ability, ability to obtain cash flow, and capital strength. The above indicators can more comprehensively reflect the enterprise's financial status in terms of short-term and long-term factors [3].

Empirical analysis of financial crisis early warning using multiple statistics

It can be seen from the cluster analysis that this article divides the research samples into three categories, so it uses a multi-category linear decision model.

The basic method of discriminant analysis

The Fisher linear discriminant function is most commonly used in discriminant analysis. Its general form is: Yi =α1x1 + α2 x2 +…αn xn + b(i =1, 2,…, k). Where k is the number of discriminant groups and Y is the discriminant score or discriminant value. x1, x2,…, xn is the dependent variable or predictor variable. a1, a2,…, anj is the coefficient of each variable (discrimination coefficient). b is a constant in the function.

The classification mechanism of Fisher's linear discriminant

Suppose there is a set X containing n d dimensional samples X = {x1,…, xn}. Among them, n1 samples belong to w1 class and denoted as X1={x11,,xn11} {X_1} = \{x_1^1,\, \cdots ,\,x_{{n_1}}^1\} . n2 samples belonging to a class w2 are denoted as X2={x12,,xn22} {X_2} = \{x_1^2, \ldots ,\,x_{{n_2}}^2\} . The basic problem to be solved by Fisher linear discrimination is to find the best projection direction. The projection of the sample in this direction can be separated most easily [4]. The problem of finding the best projection direction is mathematically the problem of finding the best transformation vector w*. J(w)=(wTSbw)/(wTSww) J(w) = ({w^T}{S_b}w)/({w^T}{S_w}w)

mi is the mean vector of various samples, mi=(1/ni)xXix,i=1,2 \matrix{{{m_i} = (1/{n_i})\sum\limits_{x \in {X_i}} {x,}} \hfill & {i = 1,2} \hfill \cr}

Therefore, maximizing the essence J (w) is to find the best direction to maximize the dispersion (numerator) between classes after projection. At the same time, minimize the intra-class dispersion (denominator) in this direction.

The classification mechanism of nuclear Fisher discriminant analysis

For most of the actual data, the method of linear discriminant analysis is too simple. Nuclear Fisher discriminant analysis uses “nuclear techniques” similar to SVM and nuclear PCA methods. First, the data is non-linearly mapped to a certain feature space F. Then perform Fisher linear discrimination in this feature space [5]. This implicitly realizes the nonlinear discrimination of the original input space. To find the linear discriminant in F, you need to maximize J(w)=wTSbΦw/(wTSwΦw) J(w) = {w^T}S_b^\Phi w/({w^T}S_w^\Phi w)

Here wF, SbΦ S_b^\Phi and SwΦ S_w^\Phi are the corresponding matrices in F, namely SbΦ=(m1Φm2Φ)(m1Φm2Φ)T S_b^\Phi = (m_1^\Phi - m_2^\Phi){(m_1^\Phi - m_2^\Phi)^T} SwΦ=i=1,2xXi(Φ(x)miΦ)(Φ(x)miΦ)T S_w^\Phi = \sum\limits_{i = 1,2} {\sum\limits_{x \in {X_i}} {(\Phi (x) - m_i^\Phi){{(\Phi (x) - m_i^\Phi)}^T}}}

In miΦ=(1ni)xXiΦ(x) m_i^\Phi = (1 - {n_i})\sum\limits_{x \in {X_i}} {\Phi (x)}

To first need to obtain the expression (3) only in the dot product form of the input samples. Then use a kernel function to replace the dot product operation. Any wF must be located in the set of all training samples in F, so an expansion of w in the following form can be found w=i=1naiΦ(xi) w = \sum\limits_{i = 1}^n {{a_i}\Phi ({x_i})}

Using the expansions (7) and (6) and replacing the dot product with the kernel function, we get wTmiΦ(1/ni)j=1nk=1niaik(xj,xki)=aTMi {w^T}m_i^\Phi - (1/{n_i})\sum\limits_{j = 1}^n {\sum\limits_{k = 1}^{{n_i}} {{a_i}k({x_j},x_k^i) = {a^T}{M_i}}}

Define (Mi)j=(1/ni)k=1n1k(xj,xki) {({M_i})_j} = (1/{n_i})\sum\limits_{k = 1}^{{n_1}} {k({x_j},x_k^i)} in the formula.

The basic steps of discriminant analysis
Using discriminant analysis to construct an early warning analysis model

It is necessary to classify the research object first [6]. We use the cluster analysis method in multivariate statistical analysis to scientifically divide listed companies in the home appliance industry into three categories according to their financial status.

The main method of establishing a discriminant model

Since there are as many as 28 sample variables for establishing the discriminant model in this paper, it is obvious that the full model method cannot be used to incorporate all of them into the discriminant function. Therefore, we need to use stepwise analysis to eliminate variables that are not significant. This will also simplify the model and improve the efficiency of discrimination. Specific discriminant analysis methods: 1) Use the system default Wilks’lambda. Each step is the entry discriminant function with the smallest λ statistic of Wilk. 2) The criterion of stepwise discrimination stops adopting the F value. When a variable is added, the variance analysis of the variables in the discriminant function is performed. 3) The unstandardized Fisher coefficient is used to discriminate and classify new samples directly. 4) Use the correlation matrix within the group when selecting the required independent variable coefficient matrix. Before calculating the correlation matrix, calculate the intra-class correlation matrix after averaging the covariance matrix of each group (class). 5) The prior probabilities in the classification parameters are equal to all prior probabilities. 6) The covariance matrix used for classification uses within-groups

Test of model establishment

We use statistical test quantity to perform a statistical test-significance test on the model to judge whether the discriminant function can separate the three categories well.

1) Tests for the equality of the means of variables in different classes. When the value of λ is 1, the mean of each group is equal [7]. The lambda values of the 6 variables in the table are all less than 1, indicating that the mean values of each group are not equal. The significance level of the six variables except for the account receivable turnover rate is less than 0.05. Therefore, the null hypothesis that the mean of each group is equal can be rejected. At the 0.05 level of significance, the mean values of 5 of the 6 variables are significantly different, and we can perform discriminant analysis.

Variable Mean Test.

Financial indicator Wilks ‘λ value F Degree of freedom 1 Degrees of freedom 2 Significance level
Roe 0.471 10.152 2 27 0.0005
Net asset interest rate 0.522 8.221 2 27 0.0016
Accounts Receivable Turnover Rate 0.887 0.179 2 27 0.2372
Turnover rate of total assets 0.684 3.722 2 27 0.0374
Main business income growth rate 0.418 12.56 2 27 0.0001
Net operating cash flow per share 0.509 8.677 2 27 0.0012

2) Test for equality of variance-covariance matrix. The test statistic is Box'sM test results shown in Table 2. The null hypothesis that the overall covariance matrices are equal is rejected at a significance level of 0.000. The variance and covariance of each category are not equal.

Box'sM test table for variance.

Box′sM 211.218
F Approx. (Asymptotically) 7.417
df1 (degree of freedom 1) 21
df2 (degrees of freedom 2) 2062.047
Sig. (Significance level) 0

3) Goodness of fit test. We use Wilks’λ statistic to test whether the mean values of the discriminant functions of each group are equal. A test of the validity of the function. Table 3 is a test of the two canonical discriminant functions constructed. The null hypothesis that the mean values of the discriminant functions of each group are equal is rejected at the significance level of 0.000. We believe that the discriminant function can distinguish the three categories well. Both canonical discriminant functions are statistically significant. It can be considered that the established discriminant function is statistically effective through the above statistical test established on the model. On this basis, the model results of the discriminant analysis can be written specifically. Otherwise, the established model is invalid.

The goodness of fit test.

Test function Wilks’ λ value Chi-square Degree of freedom Significance level
1 to 2 0.002 150.019 12 0
2 0.36 25.003 5 0
Results of establishing a discriminant model

The canonical decision function can be constructed by calculating the coefficient value of the canonical decision function. Replacing the original multiple variables with a small number of canonical variables can conveniently describe the relationship between various types [8]. The original variables can directly discriminate the Fisher discriminant function constructed by the Bayes criterion. Table 4 is the result of stepwise discriminant analysis of the obtained Fisher linear discriminant function. The Fisher linear discriminant function model containing 6 variables is obtained by removing the less important indicators from the 28 indicators (variables). The expressions of these three functions are as follows:

Y1 = 2.273X1 + 3.735X2 − 0.174X3 + 7.026X4 − 0.276X5 + 2.374X6 − 4.350

Y2 = 12.182X1 − 45.9X2 + 0.010 29X3 + 5.25X4 − 0.878X5 − 2.088X6 − 2.897

Y3 = − 774.553X1 +1722.38X2 + 4.485X3 − 146.593X4 + 67.021X5 − 50.065X6 − 1161.22

Fisher's linear discriminant function coefficient table.

Financial indicator Series
Non-financial crisis Intermediate state Financial Crisis
Roe 2.273 12.182 −774.553
Net asset interest rate 3.735 −45.9 1722.38
Accounts Receivable Turnover Rate −0.174 0.01 4.485
The turnover rate of total assets 7.026 5.25 −146.593
Main business income growth rate −0.276 −0.878 67.021
Net operating cash flow per share 2.374 −2.088 50.065
(constant) −4.35 −2.897 −1161.22

Among them Y1, Y2, Y3 represents the function discriminant value of the non-financial crisis group, the intermediate state group, and the financial crisis group. X1, X2, X3, X4, X5, X6 respectively represents the return on net assets, net asset interest rate, accounts receivable turnover rate, total assets turnover rate, main business income growth rate, and net operating cash flow per share.

The main indicators that affect the financial status of China's home appliance industry are the return on net assets and the net interest rate that reflect profitability. The account receivable turnover rate and total asset turnover rate reflect the asset management capability. The main business income growth rate reflects the growth ability. The net operating cash flow per share reflects the ability to obtain cash. Among them, two indicators reflect profitability, which accounts for one-third of the model variables. This shows that the profitability of listed companies in China's home appliance industry is particularly important. From the financial sensitivity analysis, we know that the most sensitive factor to corporate profits is the price [9]. The unprecedented fierce price wars of China's home appliance enterprises will inevitably seriously affect the enterprises’ profitability and then affect the cash capacity, debt solvency, and asset turnover ability of the enterprises. The two indicators that reflect the asset management capability in the model reflect the liquidity of corporate assets and the liquidity of corporate assets. The poor liquidity and liquidity of assets indicate that the company’s sales or cash recovery capabilities are not strong, and the efficiency of asset utilization is not high. The main business income growth rate is also a very important indicator. If an enterprise wants to seize market share to survive and develop, it must do everything possible to increase sales revenue. But on the other hand, blindly seeking to increase sales revenue, the vicious price war between companies in the industry at all costs will inevitably seriously affect the company's profitability.

Test of the use effect of the discriminant model

After the discriminant model is established, the discriminant rules must be determined. This article is a Fisher discriminant function constructed by the Bayes criterion. The category with the highest score is the corresponding category of the enterprise. For example, the three function values of Sichuan Changhong in 2020 are Y1 =1.91,Y2 = − 1.91,Y3 = − 1172.19 respectively. The maximum value is Y1, then Sichuan Changhong belongs to a non-financial crisis company. The verification methods of the discriminant function effect mainly include self-verification, external data verification, sample dichotomy, interactive verification, Bootstrap method, etc.

Self verification

Self-verification is to substitute the samples used by the constructor into the discriminant function in turn. In this way, the effect of the model can be judged. The results of self-verification are shown in Table 5.

Self-verification result table.

category Non-financial crisis Intermediate state Financial Crisis
Original value Count Non-financial crisis 12 0 0 12
Intermediate state 1 15 0 16
Financial Crisis 0 0 2 2
Verification percentage Non-financial crisis 100 0 0 100
Intermediate state 6.3 93.8 0 100
Financial Crisis 0 0 100 100
The overall classification accuracy rate is 96.7%

It can be seen from the table that the result of discriminant analysis is that the classification of 12 non-financial crisis companies is all correct. The classification accuracy rate is 100%. Only one of the 16 intermediate state companies was mistakenly classified as a non-financial crisis company. The classification accuracy rate is 93.75%. The classification accuracy of the two financial crisis companies was 100%. The overall classification accuracy rate was 96.7%. This shows that the discriminative ability of the model is better.

Interactive verification

Interactive verification is an important discriminative effect verification technology that has gradually developed in recent years [10]. The specific method is to remove one case from each category when establishing the discriminant function. Then use the established discriminant function to discriminate the case. This method can effectively avoid the interference of strong influence points.

Interactive verification result table.

Cross-authentication Category Prediction group Overall
Non-financial crisis Intermediate state Financial Crisis
Count Non-financial crisis 11 1 0 12
Intermediate state 1 15 0 16
Financial Crisis 1 1 0 2
Verification percentage Non-financial crisis 91.7 8.3 0 100
Intermediate state 6.3 93.8 0 100
Financial Crisis 50 50 0 100
The overall classification accuracy rate is 86.7%

The prediction accuracy rates of the non-financial crisis group, intermediate state, and financial crisis groups were 91.7%, 93.8%, and 0%, respectively. The correct overall rate of judgment is 86.7%. The reason why all the predictions of the financial crisis group are not correct is that the sample size of this group is small (only two companies). This affects the prediction effect of the group and the whole.

External data back-generation verification

After the discriminant function is established, a part of the sample data is collected again. We use the discriminant function to discriminate and test the discriminant effect. External data back-generation verification is due to the strong homogeneity between the 2020 and 2019 data and the 2021 data sample.

The experiment correctly predicted all 12 non-financial crisis companies. The correct rate is 100%. 15 of the 16 intermediate state companies were correctly predicted. Only one company was predicted to be a non-financial crisis company, with a correct rate of 93.8%. For 2 financial crisis companies, one was correctly predicted, and the other was predicted to be an intermediate company. The correct rate is 50%. For all 30 companies, 28 were correctly predicted, with a correct rate of 93.3%.

Judging from the three-year forecasting effect (Table 7), the forecasting accuracy of the model showed a downward trend in the three years. The closer it is to the model year, the higher the accuracy of the forecast. This is also in line with the objective law that the closer the forecast period, the better the forecast effect.

Summary of prediction model test results.

2021 2020 2019
Number of test samples 30 30 28
Check the correct number 29 28 20
Detection accuracy 96.70% 93.30% 71.40%
Misjudgment rate 3.30% 6.70% 28.60%

Even though the correct rate in the first year of the financial crisis was 96.7%, there was a misjudgment rate of 3.3%. And the farther the forecast year, the worse the accuracy. Only the size of a discriminant value cannot completely determine the financial status. The factors that affect the accuracy of discrimination include the size of the sample, the rationality of the original sample classification (grouping), the similarity (or degree of dispersion) of the sample indicators, the degree of change in financial status in different years, and so on.

Conclusion

The analysis method of this article can be used as a reference for listed companies in the home appliance industry in China and enterprises in other industries. This method can also play a certain role in listed companies’ credit rating, business performance evaluation, financial risk control, and other aspects.

Self-verification result table.

category Non-financial crisis Intermediate state Financial Crisis
Original value Count Non-financial crisis 12 0 0 12
Intermediate state 1 15 0 16
Financial Crisis 0 0 2 2
Verification percentage Non-financial crisis 100 0 0 100
Intermediate state 6.3 93.8 0 100
Financial Crisis 0 0 100 100
The overall classification accuracy rate is 96.7%

Box'sM test table for variance.

Box′sM 211.218
F Approx. (Asymptotically) 7.417
df1 (degree of freedom 1) 21
df2 (degrees of freedom 2) 2062.047
Sig. (Significance level) 0

Summary of prediction model test results.

2021 2020 2019
Number of test samples 30 30 28
Check the correct number 29 28 20
Detection accuracy 96.70% 93.30% 71.40%
Misjudgment rate 3.30% 6.70% 28.60%

The goodness of fit test.

Test function Wilks’ λ value Chi-square Degree of freedom Significance level
1 to 2 0.002 150.019 12 0
2 0.36 25.003 5 0

Fisher's linear discriminant function coefficient table.

Financial indicator Series
Non-financial crisis Intermediate state Financial Crisis
Roe 2.273 12.182 −774.553
Net asset interest rate 3.735 −45.9 1722.38
Accounts Receivable Turnover Rate −0.174 0.01 4.485
The turnover rate of total assets 7.026 5.25 −146.593
Main business income growth rate −0.276 −0.878 67.021
Net operating cash flow per share 2.374 −2.088 50.065
(constant) −4.35 −2.897 −1161.22

Interactive verification result table.

Cross-authentication Category Prediction group Overall
Non-financial crisis Intermediate state Financial Crisis
Count Non-financial crisis 11 1 0 12
Intermediate state 1 15 0 16
Financial Crisis 1 1 0 2
Verification percentage Non-financial crisis 91.7 8.3 0 100
Intermediate state 6.3 93.8 0 100
Financial Crisis 50 50 0 100
The overall classification accuracy rate is 86.7%

Variable Mean Test.

Financial indicator Wilks ‘λ value F Degree of freedom 1 Degrees of freedom 2 Significance level
Roe 0.471 10.152 2 27 0.0005
Net asset interest rate 0.522 8.221 2 27 0.0016
Accounts Receivable Turnover Rate 0.887 0.179 2 27 0.2372
Turnover rate of total assets 0.684 3.722 2 27 0.0374
Main business income growth rate 0.418 12.56 2 27 0.0001
Net operating cash flow per share 0.509 8.677 2 27 0.0012

Yuan-yuan, T. A. N., Jian-ying, C. H. E. N., & Jian, S. U. N. On Financial Crisis Warning of Listed Companies Based on CNN. Journal of Southwest China Normal University (Natural Science Edition)., 2021; 46(5): 73–80 Yuan-yuanT. A. N. Jian-yingC. H. E. N. JianS. U. N. On Financial Crisis Warning of Listed Companies Based on CNN Journal of Southwest China Normal University (Natural Science Edition). 2021 46 5 73 80 Search in Google Scholar

Papadopoulos, S., Stavroulias, P., & Sager, T. Systemic early warning systems for EU14 based on the 2008 crisis: proposed estimation and model assessment for classification forecasting. Journal of Banking Regulation., 2019;20(3): 226–244 PapadopoulosS. StavrouliasP. SagerT. Systemic early warning systems for EU14 based on the 2008 crisis: proposed estimation and model assessment for classification forecasting Journal of Banking Regulation. 2019 20 3 226 244 10.1057/s41261-018-0085-0 Search in Google Scholar

Wang, Q., Hui, F., Wang, X., & Ding, Q. Research on early warning and monitoring algorithm of financial crisis based on fuzzy cognitive map. Cluster Computing., 2019; 22(2): 3689–3697 WangQ. HuiF. WangX. DingQ. Research on early warning and monitoring algorithm of financial crisis based on fuzzy cognitive map Cluster Computing. 2019 22 2 3689 3697 10.1007/s10586-018-2219-7 Search in Google Scholar

Aghili, A. Complete Solution For The Time Fractional Diffusion Problem With Mixed Boundary Conditions by Operational Method. Applied Mathematics and Nonlinear Sciences., 2021; 6(1): 9–20 AghiliA. Complete Solution For The Time Fractional Diffusion Problem With Mixed Boundary Conditions by Operational Method Applied Mathematics and Nonlinear Sciences. 2021 6 1 9 20 10.2478/amns.2020.2.00002 Search in Google Scholar

Zhou, P., Fan, Q. & Zhu, J. Empirical Analysis on Environmental Regulation Performance Measurement in Manufacturing Industry: A Case Study of Chongqing, China. Applied Mathematics and Nonlinear Sciences., 2020; 5(1): 25–34. ZhouP. FanQ. ZhuJ. Empirical Analysis on Environmental Regulation Performance Measurement in Manufacturing Industry: A Case Study of Chongqing, China Applied Mathematics and Nonlinear Sciences. 2020 5 1 25 34. 10.2478/amns.2020.1.00003 Search in Google Scholar

Salhani, A. A PROPOSED MODEL FOR PREDICTING THE FINANCIAL DISTRESS OF PRIVATE CONVENTIONAL BANKS IN SYRIA: AN EMPIRICAL STUDY. Sciences., 2019; 4(3): 902–910 SalhaniA. A PROPOSED MODEL FOR PREDICTING THE FINANCIAL DISTRESS OF PRIVATE CONVENTIONAL BANKS IN SYRIA: AN EMPIRICAL STUDY Sciences. 2019 4 3 902 910 10.20319/pijss.2019.43.902910 Search in Google Scholar

Shang, H., Lu, D., & Zhou, Q. Early warning of enterprise finance risk of big data mining in internet of things based on fuzzy association rules. Neural Computing and Applications., 2021; 33(9): 3901–3909 ShangH. LuD. ZhouQ. Early warning of enterprise finance risk of big data mining in internet of things based on fuzzy association rules Neural Computing and Applications. 2021 33 9 3901 3909 10.1007/s00521-020-05510-5 Search in Google Scholar

Shi, Y., & Li, X. An overview of bankruptcy prediction models for corporate firms: A systematic literature review. Intangible Capital., 2019;15(2): 114–127 ShiY. LiX. An overview of bankruptcy prediction models for corporate firms: A systematic literature review Intangible Capital. 2019 15 2 114 127 10.3926/ic.1354 Search in Google Scholar

Xu, L., Qi, Q., & Sun, P. Early-Warning Model of Financial Crisis: An Empirical Study Based on Listed Companies of Information Technology Industry in China. Emerging Markets Finance and Trade., 2020;56(7): 1601–1614 XuL. QiQ. SunP. Early-Warning Model of Financial Crisis: An Empirical Study Based on Listed Companies of Information Technology Industry in China Emerging Markets Finance and Trade. 2020 56 7 1601 1614 10.1080/1540496X.2019.1703104 Search in Google Scholar

Papana, A., & Spyridou, A. Bankruptcy prediction: the case of the Greek market. Forecasting., 2020; 2(4): 505–525 PapanaA. SpyridouA. Bankruptcy prediction: the case of the Greek market Forecasting. 2020 2 4 505 525 10.3390/forecast2040027 Search in Google Scholar

Articles recommandés par Trend MD

Planifiez votre conférence à distance avec Sciendo