4.4.3 Probit models

The next experiments were carried out with probit models [9, 10]. The first constructed model was the linear probit model based on 206 banks using all the input variables. It has the following form:

$$\begin{aligned} IY &= \mathbf{C}(\mathbf{1}) + \mathbf{C}(\mathbf{2}) \ast X\_1 + \mathbf{C}(\mathbf{3}) \ast X\_2 + \mathbf{C}(\mathbf{4}) \ast X\_3 + \mathbf{C}(\mathbf{5}) \ast X\_4 \\ &+ \mathbf{C}(\mathbf{6}) \ast X\_5 + \mathbf{C}(\mathbf{7}) \ast X\_6 + \mathbf{C}(\mathbf{8}) \ast X\_7 + \mathbf{C}(\mathbf{9}) \ast X\_8 \\\\ Y &= \mathbf{1} - \text{@LLOIGSTIC}(-(\mathbf{C}(\mathbf{1}) + \mathbf{C}(\mathbf{2}) \ast X\_1 + \mathbf{C}(\mathbf{3}) \ast X\_2 \\ &+ \mathbf{C}(\mathbf{4}) \ast X\_3 + \mathbf{C}(\mathbf{5}) \ast X\_4 + \mathbf{C}(\mathbf{6}) \ast X\_5 + \mathbf{C}(\mathbf{7}) \ast X\_6 + \mathbf{C}(\mathbf{8}) \ast X\_7 + \mathbf{C}(\mathbf{9}) \ast X\_8)) \end{aligned}$$

As the experiments had shown that the inputs net interest margin (X3) and net financial result (X8) very weakly influence on the forecasting accuracy, they were excluded in the next experiments. The next probit model included six variables.

5. Conclusions

European banks.

was performed.

Author details

103

considered.

Table 27.

The problem of banks bankruptcy risk forecasting under uncertainty was

Method Total number of errors % of errors First type of errors Second type of errors

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

ANFIS 4 8 0 4 TSK 1 2 0 1 FGMDH 2 4 0 2 ARMA 9 18 4 5 Logit 8 16 2 6 Probit 7 14 2 5

fuzzy neural networks ANFIS and TSK and fuzzy GMDH, was suggested.

Comparative analysis of methods for banks bankruptcy forecasting.

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

For its solution, the application of novel methods of computational intelligence,

1. The experimental investigation of FNN TSK, ANFIS, and GMDH application in the problem of bankruptcy risk forecasting was carried out for Ukrainian and

2. The comparison of forecasting efficiency of FNN TSK and ANFIS with Fuzzy GMDH and conventional statistical methods ARMA, logit, and probit models

accuracy than statistical methods. When forecasting by one year prior to current date, fuzzy neural network TSK shows better results than FGMDH. But when forecasting for longer intervals (several years), FGMDH is the best method.

4. While in experimental investigations, the best sets of financial indicators for bankruptcy forecasting were found for Ukrainian and European banks as well.

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

3. The experimental results show that FNN and FGMDH have much better

Yuriy Zaychenko\*, Michael Zgurovsky and Galib Hamidov Igor Sikorsky Kyiv Polytechnic Institute, Kiev, Ukraine

\*Address all correspondence to: zaychenkoyuri@ukr.net

provided the original work is properly cited.

Furthermore, in this model insignificant variables debt/assets (X1) and loans/ deposits (X2) were excluded, and as a result, linear probit model with four variables was obtained.

Each of the constructed probit models was checked on the test sample of 50 banks. The results of application of all probit models are presented in Table 26.

As one may see from Table 26, the application of all the probit models gives relative error 14–18%, which is much worse than results obtained by fuzzy neural networks. It is worth to mention the decrease of model forecasting quality after exclusion of insignificant variables.
