Modeling the Stability Dynamics of Ukrainian Banking System

The article is stressed on the stability indicator of the banking system as binary variable, which takes a single value in unstable condition and non-zero value otherwise. It is offered to explore stability dynamics of Ukrainian banking system as time series, suggested to perform stability indicator on the basis of stationary time series verification by adaptation of the Forster-Stewart method to the peculiarities of the research subject. In the article it is relevant to identify the main factors of stability indicator formation, realize decomposition of a system - forming components of the variable to be explained on the base of autoregression trend-seasonal additive or multiplicative models.


Introduction
Liberalization of economic relations and expansion of globalization caused the rapid development of consumer and financial markets. At the same time, mentioned factors adversely affected the financial market and its segments, especially the banking system, because banks play the most important role in the financial market and are major financial intermediaries in our country. Besides, the fluctuation in banking sector can also be the reason of economic circumstances instability in the country. Therefore, it raises the question of necessity to carry out research and develop economical mathematical model, which could make possible to identify the factors of banking system stable development and find out the mechanism of its regulation on the basis of regression and decomposition analysis.

Research results
Modern literary analysis in the context of the banking system stability detection and evaluation [2,5,10,13,15] allows to systematize the existing approaches and consider this category as the ability of the system to maintain stable basic characteristics in time in condition of insignificant market fluctuation, to accept and resist the influence of external factors adequately, and to maintain the condition of a long-term dynamic equilibrium [1.12, 1.14]. Based on the abovementioned approach, it is suggested to transform the stability of the banking system as its ability to maintain state for a long-term dynamic equilibrium. Therefore, the purpose of this article is modeling the dynamics and forecasting stability of the banking system on the example of Ukraine.
Achieving this purpose involves the formulation and solution of the following objectives: ♦ offer a quantitative estimation (indicator) of the banking system stability characteristics; ♦ identify major factors of the dynamic stability concept formation and explore its main trends and regularitis; ♦ formalize the relationship between the seasonality (cyclicity) factors of the banking system stability and the integral indicator; ♦ to determine the influence of the stability indicator on the basic of characteristics of the the banking system functioning; ♦ forecast the stability of Ukrainian banking system within 2014-2015.
Studying the stability of the banking system requires using the input information base, which consists of the following time-series data [1.6, 1.7]: the equity capital, assets, credits and liabilities, interest incomes and net profit/(loss) during 2009-2012 years in the context of the quarterly data. These statistical data are presented in Table 1.
Let us look at the diagram of dynamics of characteristics indicators of the Ukrainian banking system, presented in Figure 1. In this illustration we can see two scales: the left one is used to display the data in the form of the bar graph, the right one − respectively, in the form of the dynamics schedules. Analysis of above-mentioned figure allows to make conclusions about the oscillation trends regarding such indicators as interest incomes and net profit/(loss), while in the context of other indicators the ongoing trend is observed. The indicated fact can be the cause of violation of the banking system stability of Ukraine.

Fig. 1. Diagram of the dynamics of input data indicators
Modeling the dynamics stability of the banking system is suggested to perform on the basis of stationary time series verification by adaptation of the Forster-Stewart method to the peculiarities of the research subject. Therefore, the stationary time series is a process, which is characterized by constant mathematical expectation and variance (without trends), autocorrelation function depends on two subsequent periods of time, but not from a specific time period. It is recommended to analyze the stages of the proposed approach practical im-plementation in more details with consideration of the mentioned definition.

Stage 1.
Creation the research information base by collecting statistical data in the context of the relevant indicators dynamics of quantitative estimation of the stability of Ukrainian banking system (see Table 2); comprehensive analysis of their basic regularities. Such indicators are: the rate of growth of net profit/loss; the capital adequacy of banks, interest margin, ROA (return on assets), ROE (return on equity) ( Figure 2).  The necessary condition for the application of Forster-Steward method for modeling the stability dynamics of the banking system is the homogeneity of the considered time-series data levels.
Homogeneity means the absence of atypical, anomalous observations, as well as the distortion of the trend. Anomalous level is a separate value of the time series, which does not correspond to the potential of the economic system, being studied, and which, while remaining the level of the time series, has a significant influence on the values of the basic characteristics of the time series. For detection of the anomalous levels of time series it is proposed to use the Irwin method. This method is based on the comparison of the time series neighbor values and the calculation of its characteristics λ t . The calculated values are compared with the critical value, λ α and if they do not exceed critical, then the corresponding levels are considered to be normal. In Table 3 the anomalous levels of the studied time series are marked with bold, which should be avoided by calculating the average value among the previous and the next relatively anomalous levels of the corresponding time series. Obtained anomalous values (in Table 3 ♦ The comprehensive analysis of time series, presented in Figure 2, allows to determine the main tendencies in change of the national banking system index stability. Therefore, clear linear trend of development is observed in the context of capital adequacy and the return on assets of banking institutions, while the seasonal variations are typical for such indices as interest margin and return on capital. The aboveindicated variations of the mentioned indicators cause the oscillation trends in the dynamics of the banking system stability indicator.

Fig. 2. Diagram of the relevant indicators dynamics of quantitative estimation of the Ukrainian banking system stability
Formalization and quantification of the revealed laws is proposed to realize with the use of mathematical methods by decomposition of the considered time series filtering trend (F(t)), seasonal (cyclic) (S) and random components.
The autoregression trend-seasonal multiplicative model of return on equity: where PM t is the interest margin at time moment t.
where ROA t is the return on assets at time moment t.
where RGP t is the rate of growth of net profit/loss at time moment t.   Table 4.
where k t (l t ) is the value of the numerical sequence k (respectively, l) at time moment t.  (Table 5). Formulas take the form of: where µ is the assessment of the mathematical expectations time series; σ 1 is the assessment of the mean-square deviations for the value c; σ 2 is the assessment of the mean-square deviations for Table 5. The dynamics of stability indicator of the Ukrainian banking system   (5) ns. With the the amount l of banking crease of the will cause the ility. A similities (critical P), in contrast effective sign s between the d in the form own, the in-97,87 billion crease of the this factor of s of the bank- The practical value of the conclusions and recommendations is the following aspects: application of the proposed model approach allows to get an early signal about the imperfection of the existing financial resources management in the context of the banking system and the correction necessity; above-established seasonality of the main factors of the banking system stability provides the opportunity to get a basis for confirmed decision-making; the linear and nonlinear regression dependencies provide the ability to describe quantitatively the regularities and prospects for achieving stability of the system.