3. The application of fuzzy neural networks for financial state forecasting

A special software kit was developed for FNN ANFIS and TSK application in bankruptcy risk forecasting problems. As input data, the financial indicators of Ukrainian banks in financial accountant reports were used in the period of 2008–2009 [2] . As the output values were used +1, for bank nonbankrupt and �1, for bank bankrupt. In the investigations, various financial indicators were analyzed, and different number of rules for FNN and the analysis of data collection period influence on forecasting accuracy were performed.

The results of experimental investigations of FNN application for bankruptcy risk forecasting are presented below.

In the first series of experiments, input data at the period of January 2008 were used (that is for two years before possible bankruptcy) and possible banks bankruptcy was forecasted at the beginning of 2010.

### Experiment No. 1:

Training sample—120 Ukrainian banks, test sample—50 banks.

Number of rules = 5.

Input data—financial indices (taken from bank accountant reports):

assets, capital, cash (liquid assets), households deposits, liabilities.

The results of application of FNN TSK are presented in Table 1.

Ap ¼ d:

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

p ¼ Aþd,

In the second stage, after fixing the values of linear parameters pkj, the actual output signals <sup>y</sup>ð Þ <sup>ℓ</sup> , <sup>ℓ</sup> <sup>¼</sup> <sup>1</sup>, <sup>2</sup>, …, L are determined using a linear equations system:

> y xð Þ <sup>ℓ</sup> � <sup>d</sup>ð Þ <sup>ℓ</sup> <sup>2</sup>

After calculating the gradient vector, a step of gradient descent method is made. The corresponding formulas (for the simplest method of the steepest descent) are

> ð Þk <sup>j</sup> ð Þ� n η<sup>c</sup>

After verifying the nonlinear parameters, the process of adaptation of linear parameters TSK (first phase) restarts and nonlinear parameters are further adapted (second stage). This cycle continues until all the parameters will be stabilized. Formulas (11)–(13) require the calculation of the gradient of the objective function with respect to the parameters of the MF. The final form of these formulas

depends on the type of MF. For example, if using the generalized bell-wise

μAð Þ¼ x

<sup>j</sup> ð Þ� n ησ

<sup>j</sup> ð Þ� n η<sup>b</sup>

1 <sup>1</sup> <sup>þ</sup> <sup>x</sup>�<sup>c</sup> σ <sup>2</sup><sup>b</sup>

the corresponding formulas for gradient of the objective function for one pair of

The error signals are sent through the network backward according to the method of back propagation until the first layer, at which gradient vector compo-

Then, the error vector ε ¼ ð Þ y � d and the criterion E are calculated:

<sup>y</sup>ð Þ <sup>L</sup> <sup>¼</sup> Ap: (9)

ð Þk <sup>j</sup> ; <sup>σ</sup>ð Þ<sup>k</sup> <sup>j</sup> ; <sup>b</sup>ð Þ<sup>k</sup> j 

<sup>∂</sup>E nð Þ ∂c ð Þk j

<sup>∂</sup>E nð Þ ∂σð Þ<sup>k</sup> j

<sup>∂</sup>E nð Þ ∂bð Þ<sup>k</sup> j

: (10)

are cal-

(11)

(12)

(13)

where A<sup>þ</sup> is a pseudoinverse matrix for matrix A.

<sup>E</sup> <sup>¼</sup> <sup>1</sup> <sup>2</sup> <sup>∑</sup> L ℓ¼1

nents of the objective function with respect to parameters c

c ð Þk

σð Þ<sup>k</sup>

bð Þ<sup>k</sup>

where n is a number of iterations.

<sup>j</sup> ð Þ¼ n þ 1 c

<sup>j</sup> ð Þ¼ <sup>n</sup> <sup>þ</sup> <sup>1</sup> <sup>σ</sup>ð Þ<sup>k</sup>

<sup>j</sup> ð Þ¼ <sup>n</sup> <sup>þ</sup> <sup>1</sup> <sup>b</sup>ð Þ<sup>k</sup>

matrix A at one step:

culated.

the following:

functions:

86

data ð Þ x; d take the form [3]:

Matrix A dimension is equal to L Nð Þ þ 1 M: By thus, a number of rows L usually is much greater than a number of columns ð Þ N þ 1 M: The solution of this equations system may be obtained by conventional methods as well as using pseudoinverse


Input data—financial indicators:

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

Results

Table 4.

Results of FNN TSK forecasting.

The results for FNN TSK are presented in Table 4.

Total number of errors 7 % of errors 10 First type of errors 1 Second type of errors 6

influence on the accuracy of forecasting; and

data was January 2008.

Experiment No. 5:

reports):

Experiment No. 6:

Results of FNN TSK forecasting.

Results

Table 5.

89

The similar experiments were carried out with FNN ANFIS.

assets, entity, cash (liquid assets), household deposits, and liabilities.

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

After analysis of the experimental results the following conclusions were made:

the variation of the number of rules in the training and test samples makes slight

the goal of the next series of experiments was to determine the optimal input data (financial indicators) for bankruptcy risk forecasting. The period of input

Number of banks and rules were the same as in previous experiment 4.

Input data—financial indicators (taken from banks financial accountant

Number of banks and rules were the same as in the previous experiment 5.

net expense on reserves and net bank profit/losses.

The results of FNN TSK application are presented in Table 5.

Total number of errors 13 % of errors 19 First type of errors 6 Second type of errors 7

profit of current year, net percentage income, net commission income; and

FNN TSK ensures the higher accuracy of risk forecasting than FNN ANFIS;
