Experiment Nos. 1–5:

Training sample = 115 banks of Europe, testing sample = 50 banks, and number of rules = 5.

Input data period = 2004 (experiment 1), 2005 (experiment 2), 2006 (experiment 3), 2007 (experiment 4), and 2007 (experiment 5).

The total results of application FNN TSK for different rules number and data collection period are presented in Table 20.

Furthermore, the similar experiments were performed with FNN ANFIS, while the period of data collection varied since 2004–2007. The corresponding results for FNN ANFIS are presented in Table 21 showing the influence of data collection period on forecasting accuracy.

After analysis of these results, the following conclusions were made:


Banks Financial State Analysis and Bankruptcy Risk Forecasting with Application of Fuzzy… DOI: http://dx.doi.org/10.5772/intechopen.82534


#### Table 20.

4.2 Application of fuzzy neural networks for European banks bankruptcy risk

Accounting and Finance - New Perspectives on Banking, Financial Statements and Reporting

The period for which the data were collected was 2004–2008. The possible bankruptcy was analyzed in 2009. The indicators of 165 banks were considered among which more than 20 banks displayed the worsening of the financial state in that year. Fuzzy neural networks and Fuzzy Group Method of Data Handling

In accordance with the above stated goal, the investigations were carried out for detecting the most informative indicators (factors) for financial state analysis and bankruptcy forecasting. Taking into account incompleteness and unreliability of input data, FNN ANFIS and TSK were suggested for bankruptcy risk forecasting. After performing a number of experiments, the data set of financial indicators was found using which FNN made the best forecast. These indicators are the following:

(FGMDH) were used for bank financial state forecasting.

debt/assets = (short-term debt + long-term debt)/total assets;

net interest margin (NIM) = net interest income/earning assets;

return on equity (ROE) = net income/stockholder equity;

cost/income = operating expenses/operating income; and

number of rules and period of data collection on forecasting results.

In the first series of experiments, FNN TSK was used for forecasting.

Input data period = 2004 (experiment 1), 2005 (experiment 2), 2006 (experiment 3), 2007 (experiment 4), and 2007 (experiment 5).

After analysis of these results, the following conclusions were made:

2. the best input variables (indicators) for European banks bankruptcy risk

1. FNN TSK has better forecasting accuracy than FNN ANFIS;

A series of experiments was carried out for determining the influence of the

Training sample = 115 banks of Europe, testing sample = 50 banks, and number

The total results of application FNN TSK for different rules number and data

Furthermore, the similar experiments were performed with FNN ANFIS, while the period of data collection varied since 2004–2007. The corresponding results for FNN ANFIS are presented in Table 21 showing the influence of data collection

return on assets (ROA) = net income/assets equity;

equity/assets = total equity/total assets.

collection period are presented in Table 20.

forecasting

loans to deposits ratio;

Experiment Nos. 1–5:

period on forecasting accuracy.

forecasting are the following:

of rules = 5.

98

Forecasting results for FNN TSK versus number of rules and data period.


#### Table 21.

Forecasting results for FNN ANFIS versus number of rules and data period.

debt/assets = (short-term debt + long-term debt)/total assets;

loans to deposits;

net interest margin (NIM) = net interest income/earning assets;

return on equity (ROE) = net income/stockholder equity;

return on assets (ROA) = net income/assets equity;

cost/income = operating expenses/operating income; and

equity/assets = total equity/total assets.

Input data collection period (forecasting interval) makes influence on forecasting results.

#### 4.3 The application of fuzzy GMDH for bank financial state forecasting

In next experiments, Fuzzy Group Method of Data Handling (FGMDH) was applied for European banks financial state forecasting. Fuzzy GMDH enables to construct forecasting models using experimental data automatically without expert [3]. The additional advantage of FGMDH is possibility to work with the fuzzy information.

As the input data in these experiments, the same indicators as in experiments with FNN TSK were used. In Table 22, forecasting results are presented in dependence on input data period collection for FGMDH


cost/income—X6;

neural networks.

4.4.2 Logit models

testing sample of 50 banks.

equity/assets—X7; and

DOI: http://dx.doi.org/10.5772/intechopen.82534

net financial result—X8.

shortened models with six and four variables.

The input data were normalized before the application. The experiments were

Each obtained model was checked on testing sample consisting of 50 banks. The comparative forecasting results for all ARMA models are presented in Table 24. As one may see in Table 24, the application of all types of linear regression models gives the same error of 18%, which is much worse than application of fuzzy

Furthermore, the experiments were performed using logit models for bankruptcy forecasting [9, 10]. The training sample consisted of 165 banks and the

The first one was constructed, linear logit model, using all the input variables.

þCð Þ 4 ∗X<sup>3</sup> þ Cð Þ5 ∗X<sup>4</sup> þ Cð Þ 6 ∗X<sup>5</sup> þ Cð Þ7 ∗X<sup>6</sup> þ Cð Þ 8 ∗X<sup>7</sup> þ Cð Þ 9 ∗X8ÞÞ

Second type of errors

Second type of errors

Total number of errors

Total number of errors

% of errors

% of errors

The next constructed model was a linear probabilistic logit model with six independent variables. The final table including the forecasting results of all the

All variables (eight) 50 5 4 9 18 Six variables 50 5 4 9 18 Four variables 50 5 4 9 18

First type of errors

First type of errors

All variables (eight) 50 6 2 8 16 Six variables 50 6 2 8 16

It has the following form (estimating and forecasting equations):

IY ¼ Cð Þþ 1 Cð Þ2 ∗X<sup>1</sup> þ Cð Þ3 ∗X<sup>2</sup> þ Cð Þ 4 ∗X<sup>3</sup> þ Cð Þ5 ∗X<sup>4</sup> þ Cð Þ 6 ∗X<sup>5</sup> þ Cð Þ7 ∗X<sup>6</sup> þ Cð Þ 8 ∗X<sup>7</sup> þ Cð Þ 9 ∗X<sup>8</sup>

Y ¼ 1 � @CLOGISTICð�ðCð Þþ 1 Cð Þ2 ∗X<sup>1</sup> þ Cð Þ3 ∗X<sup>2</sup>

logit models is presented below (Table 25)

sample

sample

Input data Testing

Comparative analysis of ARMA models.

Input data Testing

Comparative analysis of logit models.

Table 24.

Table 25.

101

carried out with full regression ARMA model, which used eight variables and

Banks Financial State Analysis and Bankruptcy Risk Forecasting with Application of Fuzzy…

Table 22.

Comparative analysis of forecasting results for FGMDH.


#### Table 23.

Forecasting results of different fuzzy methods.

If to compare the results of FGMDH with the results of FNN TSK, one can see that neural network has better accuracy at the short forecasting interval (1 year), while fuzzy GMDH has better accuracy at the greater intervals (2 or more years). This conclusion coincides with similar conclusion for Ukrainian banks.

In Table 23, the comparative results of application of different methods for bankruptcy risk forecasting are presented

## 4.4 Application of linear regression and probabilistic models

### 4.4.1 Regression models

For estimation of fuzzy methods' efficiency at the problem of bankruptcy risk forecasting the comparison with crisp method, the regression analysis of linear models was performed. As input data, the same indicators were used, which were found optimal for FNN. Additionally, the index net financial result was also included in the input set. This index makes great impact on forecasting results. Thus, input data in these experiments were eight financial indicators of 256 European banks according to their reports:

debt/assets—X1; loans/deposits—X2; net interest margin—X3; ROE (return on equity)—X4; ROA (return on assets)—X5;

Banks Financial State Analysis and Bankruptcy Risk Forecasting with Application of Fuzzy… DOI: http://dx.doi.org/10.5772/intechopen.82534

cost/income—X6;

equity/assets—X7; and

net financial result—X8.

The input data were normalized before the application. The experiments were carried out with full regression ARMA model, which used eight variables and shortened models with six and four variables.

Each obtained model was checked on testing sample consisting of 50 banks. The comparative forecasting results for all ARMA models are presented in Table 24.

As one may see in Table 24, the application of all types of linear regression models gives the same error of 18%, which is much worse than application of fuzzy neural networks.
