Entrepreneurship, Business and Economics - Vol. 2 pp 611-626 | Cite as

# Towards Valuation Multidimensional Business Failure Risk for the Companies Listed on the Bucharest Stock Exchange

## Abstract

Current research aims at developing a comprehensive financial instrument towards valuation business failure risk for a sample of 69 companies listed on the Bucharest Stock Exchange in 2013. There were considered several financial ratios such as liquidity ratios (e.g., current ratio, quick ratio, cash ratio), indebtedness ratios (e.g., general indebtedness ratio, financial stability ratio, global financial autonomy ratio, financial independence ratio, borrowing capacity ratio, long-term financial autonomy, leverage ratio, debt service coverage ratio), as well as solvency ratios (e.g., global solvency ratio and patrimonial solvency ratio). By taking into consideration the large number of selected ratios, we employed the principal component analysis as multidimensional analysis technique which ensures the non-redundant decomposition of the total variability out of the initial causal space through a lower number of components. Thereby, there were retained five principal components (being underlined liquidity, financial autonomy, financial independence, debt service coverage ratio, and solvency) which cumulate 90.5895 % of the initial information. Subsequently, based on the selected principal components we reported the aggregate business failure risk indicator.

## Keywords

Business failure risk Principal component analysis Correlation matrix Eigenvectors Eigenvalues## 1 Introduction

The financial stability of a company within a highly competitive business environment is influenced by its financial solvency at the inception, its ability, relative flexibility, and efficiency towards cash creating from its continuous operations, its access to capital markets, as well as its financial ability and standing strength when faced with unplanned cash short-falls. In fact, business failure happens when the companies record serious losses, withal the corporations becoming insolvent with liabilities, therefore generating great loss to stockholders, managers, investors, and employees (Li and Sun 2011). Therefore, we notice the inability of the corporations to pay their obligations due to inadequate working capital (Zeytinoglu and Akarim 2013).

Beaver (1966) employed a univariate research to each of the 30 different ratios by selecting a sample of 79 failed companies, as well as 79 nonfailed companies operating in 38 different industries. There was found that net income to total debt had the highest predictive ability (92 % accuracy 1 year prior to failure), followed by net income to sales (91 %) and net income to net worth, cash flow to total debt, and cash flow to total assets (each with 90 % accuracy). The first researcher who used discriminant analysis to predict the failure of firms from different industries is Altman (1968), the accuracy of the employed model towards predicting bankruptcy being estimated at 95 % 1 year prior to bankruptcy and 72 % 2 years prior to bankruptcy. Deakin (1972) showed that the model employed by Altman (1968) is better than the model applied by Beaver (1966) on the short term (1 year), whereas the model of Beaver (1966) is better on the long term (5 years), as regards the error classification rates. By considering the fact that the usefulness of accounting information is a function of the predictive ability of the information and the ability of users to interpret the data, Libby (1975) found a narrow set of financial ratios which allowed a high degree of accuracy in prediction.

Therefore, a variety of statistical techniques (such as linear discriminant analysis, LDA; multivariate discriminant analysis, MDA; quadratic discriminant analysis, QDA; multiple regression; logistic regression, logit; probit; factor analysis, FA), neural networks topologies (such as network architectures including multi-layer perception, MLP; radial basis function network, RBFN; probabilistic neural network, PNN; auto-associative neural network, AANN; self-organizing map, SOM; learning vector quantization, LVQ; cascade-correlation neural network, Cascor), as well as other intelligent techniques (such as vector machines, fuzzy logic, isotonic separation) have been applied to solve bankruptcy prediction problem (Kumar and Ravi 2007). Moreover, Tsai (2009) compared five well-known feature selection methods used in bankruptcy prediction and showed that the t-test feature selection method outperforms the correlation matrix, the stepwise regression, the principal component analysis (hereinafter ‘PCA’), and factor analysis (FA).

Current research aims at developing a comprehensive financial instrument towards valuation business failure risk for a sample of companies listed on the Bucharest Stock Exchange (BSE) by employing the PCA for an extensive set of financial ratios. According to McGurr and DeVaney (1998), financial ratios and cash flow information are chief variables as regards business failure prediction. However, gathering as much financial ratios as possible as predictors in order to make a prediction is a fundamental step in the area. The novelty of current chapter is emphasized by the financial instrument which will be developed with the purpose of valuation business failure risk related to the companies listed in Romania, being considered an extensive set of financial ratios. The utility of this study is underlined by the information provided to managers in order to set the financial policies, respectively to the investors worldwide for investment decision making.

The rest of the chapter is organized as follows. The next section provides a literature review on using PCA within financial research. Section 3 provides the research design and methodology in terms of data, variables, and statistical procedure used for the study. Empirical results of the investigation are given and discussed in Sect. 4. Some general conclusions are drawn in the last section.

## 2 Literature Review

PCA was developed by Pearson (1901), being an analogue of the principal axes theorem in mechanics and registering a noteworthy usefulness as regards exploratory data analysis and developing prediction models. Furthermore, the method was later independently developed by Hotelling (1933, 1936). Depending on the field of application, PCA it is also named the discrete Karhunen–Loève transform (KLT), the Hotelling transform, or proper orthogonal decomposition (POD). Canbas et al. (2005) proposed a methodological framework towards creating an integrated early warning system (hereinafter ‘IEWS’) which could be used for detection of banks which are facing serious problems, by selecting 40 privately owned Turkish commercial banks (21 banks failed during the period 1997–2003), being combined three parametric models (discriminant, logit, and probit) with another parametric approach, namely PCA. Therefore, PCA was employed in order to investigate the basic financial characteristics of the banks, whereas discriminant, logit, and probit models were estimated based on these characteristics to construct the IEWS. Bataille et al. (2007) applied PCA in order to extract the cyclical factors from companies’ data possibly used in the construction of the scores by the Bank de France and from these scores themselves. By employing PCA within the Turkish banking sector, Boyacioglu et al. (2009) selected 20 financial ratios with six feature groups covering capital adequacy, asset quality, management quality, earnings, liquidity, and sensitivity to market risk and retained only seven factors which explain 80.384 % of the total variance. Hu and Ansell (2009) applied sequential minimal optimization (SMO) to develop default prediction model in the US retail market. There were considered 67 potential performance variables, covering both internal and external company measures, at long last based on PCA five key principal components being retained for each of the final models. Li and Sun (2011) developed a hybrid method for business failure prediction by integrating PCA with multivariate discriminant analysis and logistic regression. There was emphasized a dominating predictive performance in short-term as regards business failure prediction of Chinese listed companies.

## 3 Research Design and Methodology

### 3.1 The Sample and Variable Selection

Initially, the dataset comprised all the companies from the exchange segment ‘BSE’, respectively 104 companies, over the year 2013. Afterwards, there were removed 20 companies from the tier ‘Unlisted’, one company from the tier ‘Int’l’, one company from the tier ‘Other Int’l’, 11 companies from financial intermediation sector (three banks, five financial investment companies, and three financial investment service companies), as well as two companies without financial data on the website related to the BSE. The industry membership of selected sample is varied as follows: wholesale/retail (4), construction (8), pharmaceuticals (4), manufacturing (20), plastics (3), machinery and equipment (8), metallurgy (3), food (2), chemicals (3), basic resources (5), transportation and storage (2), tourism (3), and utilities (4). The source of our data is depicted by the Annual financial information (key financials) which was reported on the BSE website for each company.

The description of all the variables employed within empirical research

Variable | Definition |
---|---|

| |

CR (v | Current ratio = Current assets / (Bank loans [amounts payable in a period below 1 year] + Trade suppliers [amounts payable in a period below 1 year]) |

QR (v | Quick ratio = (Current assets − Inventories) / (Bank loans [amounts payable in a period below 1 year] + Trade suppliers [amounts payable in a period below 1 year]) |

CR (v | Cash ratio = (Current assets − Inventories − Receivables) / (Bank loans [amounts payable in a period below 1 year] + Trade suppliers [amounts payable in a period below 1 year]) |

| |

GIR (v | General indebtedness ratio = Total liabilities / Total assets = (Bank loans [amounts payable in a period below 1 year] + Trade suppliers [amounts payable in a period below 1 year] + Bank loans [amounts payable in a period above 1 year] + Deferred income) / (Non-current assets + Current assets + Prepayments) |

FSR (v | Financial stability ratio = Liabilities (amounts payable in a period above 1 year) / Invested capital = Bank loans (amounts payable in a period above 1 year) / (Bank loans [amounts payable in a period above 1 year] + Shareholders’ equity) |

GFAR (v | Global financial autonomy ratio = Total liabilities / Shareholders’ equity = (Bank loans [amounts payable in a period below 1 year] + Trade suppliers [amounts payable in a period below 1 year] + Bank loans [amounts payable in a period above 1 year] + Deferred income) / Shareholders’ equity |

FIR (v | Financial independence ratio = Shareholders’ equity / (Bank loans [amounts payable in a period above 1 year] + Shareholders’ equity) |

BCR (v | Borrowing capacity ratio = Shareholders’ equity / Bank loans (amounts payable in a period above 1 year) |

LTFAR (v | Long-term financial autonomy = Liabilities (amounts payable in a period above 1 year) / Shareholders’ equity = Bank loans (amounts payable in a period above 1 year) / Shareholders’ equity |

LR (v | Leverage ratio = Total assets / Shareholders’ equity = (Non-current assets + Current assets + Prepayments) / Shareholders’ equity |

DSCR1 (v | Debt service coverage ratio1 = Gross profit or loss / Interest expense |

DSCR2 (v | Debt service coverage ratio2 = Financial year net profit or loss / Interest expense |

| |

GSR (v | Global solvency ratio = Total assets / Total liabilities = (Non-current assets + Current assets + Prepayments) / (Bank loans [amounts payable in a period below 1 year] + Trade suppliers [amounts payable in a period below 1 year] + Bank loans [amounts payable in a period above 1 year] + Deferred income) |

PSR (v | Patrimonial solvency ratio = Shareholders’ equity / Total assets = Shareholders’ equity / (Non-current assets + Current assets + Prepayments) |

### 3.2 Statistical Procedure

PCA depicts a multidimensional data analysis technique which ensures the decomposition expressed through a lower number of components (Han and Kamber 2006), as well as non-redundant of the total variability out of the initial causal space (Jolliffe 2002). The principal components are orthogonal vectors which capture as far as from the variance corresponding to the original vector variables as follows: the first principal component contains the maximum variance from the original variables’ variance, whereas the second principal component is calculated to have the second most variance, being uncorrelated (in a linear sense) with the first principal component, and so on (Hand et al. 2001; Han and Kamber 2006; Hastie et al. 2009). The initial causal space is determined by the 14 variables as regards liquidity (e.g., current ratio, quick ratio, cash ratio), indebtedness (e.g., general indebtedness ratio, financial stability ratio, global financial autonomy ratio, financial independence ratio, borrowing capacity ratio, long-term financial autonomy, leverage ratio, debt service coverage ratio), and solvency (e.g., global solvency ratio and patrimonial solvency ratio), respectively v_{1}, v_{2}, …, v_{13}, v_{14}. Therefore, each of the 69 companies listed on the BSE in 2013, selected in order to develop current empirical investigation, is distinguished through 14 variables (Witten and Frank 2005).

_{1}, v

_{2}, …, v

_{13}, v

_{14}, whereas the variances of the principal components are the eigenvalues of the covariance matrix. Furthermore, the aim is to solve the following extreme problem and the optimal criteria could be maximum or minimum depending on the nature of the function ϕ:

## 4 Empirical Results and Discussion

### 4.1 Descriptive Statistics

Descriptive statistics

N | Mean | Median | Min | Max | Std. dev. | |
---|---|---|---|---|---|---|

| ||||||

v | 69 | 5.862 | 2.717704 | 0.058 | 75.49 | 10.35 |

v | 69 | 4.474 | 1.639651 | 0.04 | 74.72 | 9.77 |

v | 69 | 2.428 | 0.212318 | 0.003 | 72.51 | 9.06 |

| ||||||

v | 69 | 0.297 | 0.223472 | 0.005 | 1.5 | 0.29 |

v | 69 | 0.113 | 0.012258 | −2.512 | 3.59 | 0.56 |

v | 69 | 0.307 | 0.208123 | −10.927 | 9.76 | 2.07 |

v | 69 | 0.887 | 0.987742 | −2.594 | 3.51 | 0.56 |

v | 69 | 8.255 | 0.308626 | −222.434 | 233.57 | 43.83 |

v | 69 | 0.041 | 0.004281 | −5.037 | 3.24 | 0.79 |

v | 69 | 1.147 | 1.376204 | −16.282 | 17.32 | 3.75 |

v | 69 | 2036.403 | 0.603585 | −269.187 | 93,450.54 | 12,162.36 |

v | 69 | 1633.504 | 0.364559 | −269.187 | 76,225.61 | 9831.07 |

| ||||||

v | 69 | 12.867 | 4.474824 | 0.667 | 207.78 | 27.79 |

v | 69 | 0.475 | 0.624888 | −1.665 | 0.96 | 0.51 |

_{1}and v

_{2}(0.975), v

_{1}and v

_{3}(0.934), v

_{1}and v

_{13}(0.946), v

_{2}and v

_{3}(0.969), v

_{2}and v

_{13}(0.964), v

_{3}and v

_{13}(0.937), v

_{6}and v

_{9}(0.917), v

_{6}and v

_{10}(0.850). Moreover, the strong correlations between the selected variables mitigates the individual meaning of the variables and emphasizes the presence of informational redundancy. Thereby, PCA is employed with the purpose of reducing the dimensionality of the initial causal space, also considering a minimum loss of information.

Correlation matrix

v | v | v | v | v | v | v | v | v | v | v | v | v | v | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

v | 1 | |||||||||||||

v | (0.000) | 1 | ||||||||||||

v | (0.000) | (0.000) | 1 | |||||||||||

v | (0.002) | (0.007) | (0.056) | 1 | ||||||||||

v | (0.770) | (0.699) | (0.742) | 0.191 (0.115) | 1 | |||||||||

v | (0.689) | (0.736) | (0.780) | (0.516) | 0.039 (0.752) | 1 | ||||||||

v | 0.036 (0.770) | 0.047 (0.699) | 0.040 (0.742) | (0.115) | (0.000) | (0.752) | 1 | |||||||

v | (0.768) | (0.836) | (0.802) | (0.004) | (0.871) | 0.093 (0.449) | 0.020 (0.871) | 1 | ||||||

v | (0.899) | (0.929) | (0.923) | (0.298) | (0.145) | (0.000) | 0.177 (0.145) | 0.007 (0.956) | 1 | |||||

v | (0.846) | (0.913) | (0.906) | (0.799) | 0.074 (0.544) | (0.000) | (0.544) | 0.087 (0.480) | (0.000) | 1 | ||||

v | 0.137 (0.261) | 0.125 (0.305) | 0.080 (0.514) | (0.274) | (0.768) | (0.906) | 0.036 (0.768) | (0.799) | (0.947) | 0.023 (0.851) | 1 | |||

v | 0.132 (0.280) | 0.120 (0.326) | 0.076 (0.536) | (0.279) | | (0.908) | 0.036 (0.767) | (0.800) | (0.948) | 0.023 (0.849) | (0.000) | 1 | ||

v | (0.000) | (0.000) | (0.000) | (0.003) | (0.532) | (0.687) | 0.077 (0.532) | (0.815) | (0.915) | (0.848) | 0.097 (0.427) | 0.092 (0.451) | 1 | |

v | (0.015) | (0.032) | 0.202 (0.096) | (0.000) | (0.210) | 0.146 (0.232) | 0.153 (0.210) | (0.001) | 0.109 (0.373) | (0.045) | 0.058 (0.638) | 0.056 (0.646) | (0.014) | 1 |

### 4.2 The Results of Principal Component Analysis

Eigenvalues of the correlation matrix and related statistics

Value number | Eigenvalue | % Total variance | Cumulative Eigenvalue | Cumulative % |
---|---|---|---|---|

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

6 | 0.649445 | 4.63890 | 13.33198 | 95.2284 |

7 | 0.366657 | 2.61898 | 13.69864 | 97.8474 |

8 | 0.146135 | 1.04382 | 13.84477 | 98.8912 |

9 | 0.053664 | 0.38331 | 13.89843 | 99.2745 |

10 | 0.051539 | 0.36814 | 13.94997 | 99.6427 |

11 | 0.036598 | 0.26142 | 13.98657 | 99.9041 |

12 | 0.013189 | 0.09421 | 13.99976 | 99.9983 |

13 | 0.000239 | 0.00170 | 14.00000 | 100.0000 |

Thus, we notice that after the fifth point out of the above graph, which depicts the fifth principal component, the slope is decreasing. Furthermore, according to Kaiser (1960) criterion, there are retained only the principal components which correspond to the eigenvalues greater than one. Hence, based on the graph revealed in Fig. 1, as well as Kaiser (1960) criterion, we will retain five principal components.

Factor coordinates of the variables, based on correlations

F | F | F | F | F | |
---|---|---|---|---|---|

v | | −0.119463 | −0.175794 | −0.040418 | 0.090462 |

v | | −0.121383 | −0.187470 | −0.054548 | 0.127763 |

v | −0.917998 | −0.135080 | −0.220863 | −0.088476 | 0.175321 |

v | 0.526955 | −0.272281 | −0.315411 | 0.047821 | 0.552125 |

v | 0.172186 | −0.189849 | | 0.266501 | −0.361835 |

v | 0.002415 | | −0.296022 | 0.051232 | 0.147434 |

v | −0.172186 | 0.189849 | | −0.266501 | 0.361835 |

v | −0.075129 | 0.238316 | 0.167204 | −0.110827 | |

v | −0.043759 | | −0.108191 | −0.009713 | 0.290320 |

v | −0.024082 | 0.854492 | −0.311309 | 0.094372 | 0.080239 |

v | −0.232195 | 0.013118 | 0.269572 | | 0.028042 |

v | −0.227470 | 0.013990 | 0.271030 | | 0.027571 |

v | −0.950079 | −0.113614 | −0.153447 | −0.091189 | 0.109282 |

v | −0.461809 | 0.371213 | 0.240066 | −0.101447 | |

The strong relationship expressed by the first (−0.954663) and by the second correlation coefficient (−0.956570) out of the first column from Table 5 emphasizes that the first principal component conveys the informational content of the original variables v_{1} and v_{2}. Likewise, the second principal component expresses the informational content of the original variables v_{6} and v_{9}, the third principal component expresses the informational content of the original variables v_{5} and v_{7}, the fourth principal component conveys the informational content of the original variables v_{11} and v_{12}, whereas the fifth principal component conveys the informational content of the original variables v_{8} and v_{14}. Therefore, the first principal component (F_{1}) underlines a synthetic **indicator of liquidity**, the second principal component (F_{2}) is interpreted as an **indicator of financial autonomy**, the third principal component (F_{3}) is an **indicator of financial independence**, the fourth principal component (F_{4}) is an **indicator of debt service coverage ratio**, whereas the fifth principal component (F_{5}) is construed as an **indicator of solvency**.

Eigenvectors of the correlation matrix

V | F | F | F | F | F |
---|---|---|---|---|---|

v | −0.463853 | −0.071493 | −0.120825 | −0.029005 | 0.071608 |

v | −0.464780 | −0.072642 | −0.128850 | −0.039145 | 0.101135 |

v | −0.446039 | −0.080839 | −0.151801 | −0.063494 | 0.138781 |

v | 0.256038 | −0.162946 | −0.216785 | 0.034318 | 0.437053 |

v | 0.083662 | −0.113615 | −0.585436 | 0.191251 | −0.286422 |

v | 0.001174 | 0.552618 | −0.203458 | 0.036766 | 0.116706 |

v | −0.083662 | 0.113615 | 0.585436 | −0.191251 | 0.286422 |

v | −0.036504 | 0.142620 | 0.114921 | −0.079534 | −0.545135 |

v | −0.021262 | 0.537936 | −0.074361 | −0.006970 | 0.229812 |

v | −0.011701 | 0.511371 | −0.213966 | 0.067724 | 0.063516 |

v | −0.112820 | 0.007851 | 0.185279 | 0.669573 | 0.022197 |

v | −0.110524 | 0.008372 | 0.186282 | 0.670104 | 0.021825 |

v | −0.461626 | −0.067992 | −0.105466 | −0.065440 | 0.086506 |

v | −0.224385 | 0.222153 | 0.164999 | −0.072802 | −0.483942 |

The score matrix is disclosed in the Appendix 1. Thus, based on the principal components’ coefficients, there were computed the scores related to the observations in the space of the principal components. The coordinates of the objects in the new space, respectively the projections of the objects on the space’ axes, are the valuations of the objects in relation with the new variables, being entitled the scores of the principal components. By taking into consideration the informational content, we will compute the coefficients of importance for each of the five principal components. Thereby, we mark as CI_{1} the coefficient of importance related to the first factor, as well as var(\( {\mathrm{w}}_1\Big) \) denotes the variance corresponding to the first principal component, CI_{1} = var(\( {\mathrm{w}}_1\Big) \)/\( \sum_{\mathrm{j}=1}^5\mathrm{v}\mathrm{a}\mathrm{r}\left({\mathrm{w}}_{\mathrm{j}}\right) \), thus ensuing the following values for the coefficients of importance: CI_{1} = 0.3340; CI_{2} = 0.2202; CI_{3} = 0.1669; CI_{4} = 0.1531; CI_{5} = 0.1258.

Therefore, the Appendix 2 provides the values of the aggregate business failure risk indicator (hereinafter ‘ABFRI’) for the companies listed on the BSE in 2013. The ABFRI was computed as following: ABFRI = \( \sum_{\mathrm{j}=1}^5{\mathrm{C}}_{\mathrm{i}}\left(\mathrm{j}\right) \)*F_{j}.

## 5 Concluding Remarks

By selecting a set of variables which comprised 14 financial ratios as regards liquidity, indebtedness, as well as solvency, related to 69 companies listed on the BSE in 2013, we employed PCA in order to develop a comprehensive financial instrument towards valuation business failure risk. Therefore, five principal components were retained, being underlined liquidity, financial autonomy, financial independence, debt service coverage ratio, alongside solvency, which cumulate 90.5895 % of the initial information. Subsequently, based on the selected principal components we computed the aggregate business failure risk indicator. The limitations of current empirical investigation are depicted by the short period of research. As future research avenues, we propose the development of a neural network model for business failure prediction, alongside employing the traditional statistical techniques, aiming at comparing the registered results.

## Notes

### Acknowledgement

This work was cofinanced from the European Social Fund through Sectoral Operational Programme Human Resources Development 2007–2013, project number POSDRU/159/1.5/S/134197 “Performance and excellence in doctoral and postdoctoral research in Romanian economics science domain”.

## References

- Altman, E. I. (1968). Financial ratios, discriminant analysis and the prediction of corporate bankruptcy.
*The Journal of Finance, 23*(4), 589–609.CrossRefGoogle Scholar - Bataille, E., Bruneau, C., & Michaud, F. (2007). Business cycle and corporate failure in France: Is there a link?
*Computational Economics, 29*(2), 173–197.CrossRefGoogle Scholar - Beaver, W. H. (1966). Financial ratios as predictors of failure.
*Journal of Accounting Research, 4*, 71–111.CrossRefGoogle Scholar - Boyacioglu, M. A., Kara, Y., & Baykan, O. K. (2009). Predicting bank financial failures using neural networks, support vector machines and multivariate statistical methods: A comparative analysis in the sample of savings deposit insurance fund (SDIF) transferred banks in Turkey.
*Expert Systems with Applications, 36*(2), 3355–3366.CrossRefGoogle Scholar - Canbas, S., Cabuk, A., & Kilic, S. B. (2005). Prediction of commercial bank failure via multivariate statistical analysis of financial structures: The Turkish case.
*European Journal of Operational Research, 166*(2), 528–546.CrossRefGoogle Scholar - Cattell, R. B. (1966). The scree test for the number of factors.
*Multivariate Behavioral Research, 1*(2), 245–276.CrossRefGoogle Scholar - Deakin, E. B. (1972). A discriminant analysis of predictors of business failure.
*Journal of Accounting Research, 10*(1), 167–179.CrossRefGoogle Scholar - Han, J., & Kamber, M. (2006).
*Data mining: Concepts and techniques*(2nd ed.). San Francisco: Morgan Kaufmann.Google Scholar - Hand, D., Mannila, H., & Smyth, P. (2001).
*Principles of data mining*. Cambridge, MA: MIT Press.Google Scholar - Hastie, T., Tibshirani, R., & Friedman, J. (2009).
*The elements of statistical learning: Data mining, inference, and prediction*(2nd ed.). New York: Springer.CrossRefGoogle Scholar - Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components.
*Journal of Educational Psychology, 24*(6), 417–441.CrossRefGoogle Scholar - Hotelling, H. (1936). Relations between two sets of variates.
*Biometrika, 28*(3/4), 321–377.CrossRefGoogle Scholar - Hu, Y.-C., & Ansell, J. (2009). Retail default prediction by using sequential minimal optimization technique.
*Journal of Forecasting, 28*(8), 651–666.CrossRefGoogle Scholar - Jolliffe, I. T. (2002).
*Principal component analysis*(2nd ed.). New York: Springer.Google Scholar - Kaiser, H. F. (1960). The application of electronic computers to factor analysis.
*Educational and Psychological Measurement, 20*(1), 141–151.CrossRefGoogle Scholar - Kumar, P. R., & Ravi, V. (2007). Bankruptcy prediction in banks and firms via statistical and intelligent techniques—A review.
*European Journal of Operational Research, 180*(1), 1–28.CrossRefGoogle Scholar - Li, H., & Sun, J. (2011). Empirical research of hybridizing principal component analysis with multivariate discriminant analysis and logistic regression for business failure prediction.
*Expert Systems with Applications, 38*(5), 6244–6253.CrossRefGoogle Scholar - Libby, R. (1975). Accounting ratios and the prediction of failure: Some behavioral evidence.
*Journal of Accounting Research, 13*(1), 150–161.CrossRefGoogle Scholar - McGurr, P., & DeVaney, S. (1998). Predicting business failure of retail firms: An analysis using mixed industry models.
*Journal of Business Research, 43*(3), 169–176.CrossRefGoogle Scholar - Pearson, K. (1901). On lines and planes of closest fit to systems of points in space.
*Philosophical Magazine, 2*(11), 559–572.CrossRefGoogle Scholar - Tsai, C.-F. (2009). Feature selection in bankruptcy prediction.
*Knowledge-Based Systems, 22*(2), 120–127.CrossRefGoogle Scholar - Witten, I. H., & Frank, E. (2005).
*Data mining: Practical machine learning tools and techniques*(2nd ed.). San Francisco: Morgan Kaufmann.Google Scholar - Zeytinoglu, E., & Akarim, Y. D. (2013). Financial failure prediction using financial ratios: An empirical application on Istanbul Stock Exchange.
*Journal of Applied Finance & Banking, 3*(3), 107–116.Google Scholar