Methods for prediction of economic crises in the global economy and financial centers

The paper studies the issues pertaining to the timely identification of economic crises under conditions of globalization. It offers an integral indicator of the economy’s development level (global economy and financial centers), carries out the filtering of the trend and systemic components of this indicator’s time series, which makes it possible to determine the cyclicity of crises and to predict the min short-term and long-term perspective. It introduces the indicator to formalize and quantify the crises on the global scale and in the three major financial centers (the United States, Europe and Asia). It also examines the adequacy of the proposed approach based on the dynamics of the global crises over the past 50 years.


Introduction 1
With the transformation of the global financial architecture the strengthening of integration processes within the national and international financial markets is occurring. Along with the free movement of the capital, goods and services the crisis phenomena and their destructive impact on the economy are increasing. Therefore, the need for preliminary identification, monitoring and development of measuresto mitigate the negative effects of the market, interest rate, currency, political and other risks determines the necessity of forming the instruments of economic and mathematical modeling and forecasting of crises.

The main results of the research
In the recent decades the economic development has been accompanied by the search for instruments of an early warning and detection of imbalances in the national economies. Integration processes, which have covered the whole range of social activities, led to the rapid expansion of destructive factors both within and outside individual countries. Crisis phenomena on certain markets destabilize the effective functioning of the whole financial system of a country. The high level of interconnection and interpenetration of domestic and international financial markets leads to the negative synergistic effect and the loss of equilibrium by the entire global economy.
The identification of sources of financial instability at the level of individual countries and financial centers is the basis for the prevention of possible shocks to the global economy. The forecasting of crisis at the local level makes it possible to reduce financial losses and, considering the characteristic features and economic potential of the regions, im-Olha Kozmenko, Olha Kuzmenko, 2013 prove the effectiveness of preventive measures. The forecasting of the cyclicity of the world economy also serves as an essential element of effective crisis assessment and prevention systems. This is connected to the ability to form a coherent strategy for an early detection of crises and to create conditions for overcoming their consequences.
Therefore, the formation of scientific and methodical approach for the formalization of the process of prediction of global economic crises under conditions of integration is becoming increasingly relevant.
Based on the importance of this problem we propose a methodology for the forecasting of crises in the global economy. We will consider the stages of this methodology.

Stage 1.
Formation of the knowledge base of research -relevant indicators of the level of development of the world economy and its three financial centers (the United States, Europe and Asia [2]). Selection of data about the financial centers and a further study of peculiarities of crisis forecasting within national economies caused by the different mentality of the population and the structure of financial systems. As a knowledge base of the proposed approach we consider the data describing the development of the world economy during the period 1960-2012 and serving directly or indirectly as indicators of crises. The source of the input information base for our research is the website of the World Bank [9]. Similar tables have been drawn up for the financial centers. Table 1 to comparable form. As input indicators have different effects on the resultant indicator and have different measurement units, it is proposed to normalize the input data base through the use of the following mathematical correlations: for destimulating indicators -savage normalization:

Stage 2. Bringing the indicators of
where C it is a relevant indicator of the global economy's (financial centers') development level characteristics during the t-year; NC itnormalized value of the indicator during the t-year; for stimulating indicators -natural normalization: ( The results of realization of this stage for the world economy are presented in Table 2 (See Appendix).  Table 2. It is assumed that the weight of the input information base indicators will be the same. Thus, at this stage the calculations will be conducted by using the following formula: where IIC(t) is an integral indicator of the level of economic development (world economy or a certain financial center) in the period t.
Practical results of implementation of the abovementioned approach, namely, the calculated values of the integral indicator of the economy's development level for each year in the period of 1960-2012 are presented in graphical form ( Figure 1 in Appendix).
On the basis of the graphical analysis we made the following conclusions: There is a growing oscillating trend in the indicator. This shows the progressive development of the economy and realization of the existing potential despite certain periods of financial instability. One can observe a cyclical change of the indicator making it possible to identify the periods of economic booms and recessions. There are periodic changes in the leading position among the American and the European financial centers; countries, which form the Asian financial center, demonstrate the record growth of economic development.  Table 3 in Appendix). Based on systematization of the existing approaches to defining crises, their factors, negative consequences and duration [2,3,5,9,10,12] in the period 1960-2012, we will consider the international financial crises, the characteristics of which are presented in Table 3.
Thus, over the past 50 years there have been 4 global economic crises, the biggest of which was the crisis of 2008-2010.

Stage 5.
Selection and justification of the crisis indicator as an indicator, which makes it possible to predict with the highest degree of accuracy the occurrence of a crisis and to make appropriate managerial decisions to counteract it [12]. As the indicator shows the average trend, it is proposed to analyze its derivatives in order to interpret the crises [6].
We consider different approaches to determining the crisis indicator. On the basis of identification of their main advantages and drawbacks we will formulate the basic requirements for the application of these methods. For example, as a crisis indicator we consider the value of the chain growth rate time series for the integral indicator of the economic development ( Figure 2 in Appendix).
The analysis of data ( Figure 2) reveals all crisis periods (shown in Table 3 The crisis indicator may be the testing of the anomalous levels of the global economy's integral indicator [8] according to the Irwin method ( Figure 3). On the basis of the graphical analysis we discover that the anomalous levels of the ICC indicator are the values of the crisis periods, which are characterized by a significant deviation from its average value. Considering the fact hat the database ( Figure 3) can help reveal all crisis periods from 1960 to 2012, it would be right to regard it as a crisis indicator.
Thus, one could argue that the most informative indicator in terms of identifying crisis phenomena seems to be the anomalous levels of time series. Based on the comparison of the data ( Figure 4) and major financial shocks (Table 3), it can be argued that the obtained results with their marginal deviations and with the time lag between the initial impact of the factor and its subsequent effects correspond to the actual statistical data, confirming the expediency of using the developed crisis indicator in crisis forecasting. [1,11]. The realization of this stage gives an opportunity to determine the trend in the changes of the indicator, the cyclicity of crises and to get a mathematical provision in the form of regression equations for predicting the anomalous levels and making decisions regarding the preventive measures. Thus, it is proposed to detect the presence of systematic components of the tested time series based on the correlogram for first differences ( Figure 5 in Appendix).

Stage 7. Decomposition of time series for the values of the IIC indicator
The dependence of autocorrelation coefficients on the value of the time lag shows the following: Autocorrelation coefficient for the time lag of one year is statistically significant, which (though not showing the cyclicity of crises) confirms the lag of information flow. Autocorrelation coefficient for the time lag of 4 years is statistically significant, i.e. the cyclicity of crises and anomalous values of the crisis indicator are characterized by the time interval of 4 years.
In its turn, the correlogram of zero differences for the IIC indicator's successive values demonstrates the specification of unsystematic component (trend) of this time series in the form of second-degree polynomial. Statistical estimations of the parameters of nonlinear regression for the trend component, the corresponding standard errors, the confirmation of the statistical significance of coefficients and their intervals are presented in Table 5 (See Appendix).
Thus, on the basis of the data in the column "Coefficients" of Table 5 where IIC W (t) is an integral indicator of the level of the global economic development in the period t; I 1 (I 2 , I 3 , I 4 ) is an indicator of each of the first (second, third, fourth) year since 1960 at intervals of 4 years, which adopts a unit value in the described case and a zero value in the opposite case.
The characteristic of the cyclic component (equation (5)

Stage 9. Prediction of values of integrated indicators for the global economy's and financial cen-
ters' development level in the period from 2013 to 2020 and determination of anomalous values for thesetime series as indicators of crisis phenomena in accordance with the Irwin method [13]. It is proposed to systematize the results of the calculations and present them in a tabular formin the context of the two research methods: decomposition analysis (Table 6) and autoregressive analysis ( Table 7 in Appendix).
The analysis of the data in Table 6  The results of the integral indicator autoregressive analysis show with a slight deviation a similar trend regarding the periodization, duration and cyclicity of crises that have been identified through the method of decomposition analysis (Table 7). Stage 10. Development of a system of preventivemeasures to counteract the destructive factors of crises. The proposed instruments for crisis forecastingmake it possible to develop an effective set of measures against destructive influences. The availability of information about the periods of a crisis, its duration and expansion characteristics, creates an opportunity for supranational regulation of the process of counteraction to financial instability and, as a result, reduction of economic losses for individual states from crises.

Conclusions
The paper proposes: a crisis indicator on the basis of the Irwin test to examine the anomalous levels of time series; an integral indicator for the development level of the global economy and three major financial centers (American, European and Asian) on the basis of decomposition and autoregressive analysis making it possible to conduct an adequate prediction of crises under international integration. The proposed methods are the basis for effective decision-making regarding the development of measures to prevent crises and minimize their impact on the macro level. Note: * Destimulating indicators (the growth of the indicator means stagnation (the decline means development)). ** Stimulating indicators (the growth of the indicator means development (the decline means stagnation)).