POSSIBILITIES OF APPLICATION OF THE COMPLEX INDEX AT THE STOCK MARKET STATISTICAL PREDICTION

The concept "stock market" from the point of view of the subjects operating on it, is aggregated, compound, including in the structure the numerous types of indexes, which ultimate goal of the analysis is to describe the predicted cash flow. In our opinion, exactly the forecast of the cash flow is the fundamental purpose, as in the creation of mathematical models of the stock market, and at the prediction of its separate indexes. The above mentioned purpose is fully answered by the descriptive statistics technique, and in particular the dispersion analysis. It is also possible to refer the comparative ease of carrying out the analysis to the advantages of this technique at the small span time and availability of the software to the data set analysis. The dispersion analysis is the invariable component when carrying out the fundamental analysis and the analysis of portfolio risks.

But as it is known, the analytical information in itself does not carry any amount of the significant advantage without interpretation, or explanation according to the purpose of carrying out such-like researches. At the same time, the specifics of the stock market itself always carries in itself such lines as risk and indeterminacy which are quite difficult for predicting at the application of the formalized statistical models.

Unreasonable and as a result the improper choice of the mathematical apparatus, generally leads to an inaccuracy of the created mathematical models, receiving insecure results in the process of their application and, respectively, there is a mistrust to the received results, and conclusions on their basis are ignored.

Therefore, for the efficient and targeted carrying out the analysis it is necessary to define those mathematical criteria which influence on the accuracy of the predicted cash flows.

It is also apparent that the requirement of the input data determinacy is the unjustified simplification of the reality as any complex index is characterized by a set of factors of indeterminacy: indeterminacy of the input data, indeterminacy of the environment, indeterminacy connected with the character, options and model of the market participants. Factors of the indeterminacy define the investor risk that is danger of loss of the resources. In the analysis of the long-term prediction indexes, including on the basis of the statistical data, it is necessary to analyze a condition of the large number of indeterminate parameters of the market conditions for the long-lived period of time and therefore the absolutely precise forecast at the high dispersion cannot almost be received.

The logic of carrying out the analysis with the use of complex indexes method means carrying out the sequential stepwise analysis (picture 1).

Picture 1 - Algorithm of the stock market forecast model creation on the basis of a comprehensive approach of the input data for the dispersion analysis choice

At the first stage it is necessary to create the criteria tables, for example profitability of assets on the groups. And, if there is an opportunity to reveal the forecast and actual indexes of last periods, it is expedient to use both types of the criteria.

At the second stage on the basis of the chosen criteria the complex index that will be considered in more detail further is formed. Data on the index for the period are also formed in the table, at the same time, the table with recommended, or desirable values, and also permissible variations is formed.

At the third stage the immediately statistical analysis is carried out. It is expedient to carry out this procedure in the MS Office applications, or Statistics, first of all from the point of view of accuracy and speed of the receiving result.

At the fourth stage the comparison of the analysis results to the table data for the analysis is carried out, the result is interpreted and the research summary is concluded.

As for the complex index choice, in the matter it is necessary to be guided by a method of expert estimation with after-treatment of data by the indistinct and interval method.

The given method is actual for using of the statistics indicators first of all due to that it is more applicable to the indeterminacy conditions when the boundaries of values of the analyzed parameter within which it can change are reasonably precisely known only, but at the same time there is no quantitative or qualitative information on the opportunities or probabilities of realization of its various values in the given interval. According to this method, the input variables are set in the form of the intervals whose membership functions are classical characteristic functions of a set, therefore further the direct application of rules of the indistinct mathematics for receiving a resultant efficiency factor in an interval kind is possible. In the interval method it is offered to take the value of the maximal damage per the unit of indeterminacy for the risk degree [2, page 25]:

, (1)

whereis the parameter’s desired value;

is the minimum parameter’s value;

is the maximum parameter’s value;

is the risk degree, or the ratio of the distance from the requiredvalue to its minimum or maximal one to an interval between its maximal and minimum values.

Below the main advantages of the given approach to the creation of statistical arrays in dispersion analysis are listed:

1. The given approach allows to formalize in the indivisible form and to use all the available non-uniform information that increases reliability and quality for the choice in the strategic decisions;

2. The given method similarly to the Monte-Carlo method forms the total spectrum of possible scenarios of the stock market development, and not just the lower and upper limits of the indexes fluctuations, thus the investment decision is made not on the basis of two estimates, but on all set of the estimates.

3. The given method allows the value of the negative results from investment activity - the risk degree;

4. The method does not require absolutely precise set up of the membership functions as unlike the probability methods, the result received on the basis of the indistinct and interval method is characterized by the low sensitivity to the change of the membership functions type of the initial indistinct numbers that in the actual practice of the poor quality of the initial information of the domestic companies activity on the stock market and derivatives, does the application of this method more attractive;

5. Usually, the initial information about the investment domestic companies as well as about the dynamics of the market as a whole is represented quite poor that compels to carry out the prediction model operation with the small statistical selections. Calculation of the indexes on the basis of the indistinct and interval method is efficient in the situations when the probabilistic estimates cannot be received that always takes place at the preliminary estimate of the long-term tendencies and is rather often — in the subsequent perspective analysis which is carried out in the absence of sufficient informational base.

Thus, the algorithm of carrying out the preparation directly to a statistical analysis is resulted to the following view (picture 2).

Picture 2-Step-by-step technique of receiving a complex index for carrying out a statistical analysis

As a result of carrying out the above-named step-by-step selection the matrix of complex indexes is formed (table 1).

Table 1 - Analytical matrix of the complex indexes for further statistical processing

Name of the index characteristics	Data set ups analysis levels
Criteria level	According to actual data	According to the predicted data
Rating assessment
Index components
Necessary economic effect (profitability and risk ratio)

If to consider from the practical application point of view, the given method despite the apparent complexity in view of its multi-staging has the indisputable advantage.Consideringnotseparatecriteria, butthe complexindexes, bymeansofthistechniquetheinitialtargetindexesfromapositionofthefinancialeffectincludedinabasisoftheforecastare combined. Further it is estimated, as an example by a method of F-test or by the complete toolkit of the descriptive statistics a number of the cumulative criteria from a point of view of their influence on this or that individual criterion, that is the procedure of model prediction actually becomes more simple, and the models received as a result can have as point-wise descriptive character, and to describe the ratios of the separate indexes on the complex and vice versa. Therefore, having worked to analyze the criteria from the point of view of their efficiency for the research object, it is possible to reduce the process of carrying out model prediction and essentially to increase its value for the subsequent analysis, thus without using the specialized analytical platforms.

Thus, the given method allows to receive the total indicators with that set of the characteristic which better answers to the purposes of the conducted statistical research, to build multi-variant model and does results as much as possible useful to further analytical work.

REFERENCES:

1) Watsham T. J. Parramore K. The quantitative methods in the finance: Trans. from Engl. – M.: UNITY. Finance, 2009

2) Kochovich E. Financial mathematics. – M.: Finance and statistics, 2012

3) Druzhinin N.K. Mathematical statistics in the economy. – M.: Statistics, 1971