The analysis of a situation in the country is spent by means of the most comprehensive macroeconomic parameters: the gross domestic product, inflation, quality of a life, employment, etc. And carrying out of successful economic policy depends on reliability of their forecasts.

Gross domestic product - a parameter of the generaleconomic condition of the country, market cost of the goods intended for final use and the services made in territory of the given country for the certain period of time and reflecting real contribution of the enterprises in creation of concrete products, i.e. a wages, profit, amortization, interest for the credit, etc. gross domestic product is total of a condition of economy, and significant influence renders on share indexes and a monetary and credit policy of the central bank and the government, is used at calculations of the minimal wages, the future tax revenues and other important parameters.

But official statistical given gross national products move more than with annual delay, therefore there is a necessity of its calculation on the basis of existing data. That is the urgency of the decision of the given task of forecasting is obvious.

The choice of optimum amount of factors of influence and the analysis of quantitative and qualitative parameters of their influence is the primary goal at construction of a forecasting model of gross domestic product.

Gross domestic product is estimated both in the actual (current) prices, and in the constant (comparable) prices. One of the major tasks of statistics is recalculation of a parameter of gross national product and its components from the actual prices in constants. It is connected by that on change of volume of gross national product in the actual prices influence renders not only change of amount of the made or used goods and services, but also change of the prices for the goods and services. For calculation of gross national product in real terms there are different methods of reassessment, in particular, the method of extrapolation based on use of indexes of physical volume, is used in case of absence of the information on the prices, but thus there are data about change of volumes of output or the rendered services.

Index of physical volume of gross domestic product name a parameter which represents the attitude of volumes of gross national product of the given and previous periods expressed in same stable prices:

I_p.v.GDP = GDP₁ / GDP₀ = Σp₀q₁ / Σp₀q₀

where GDP₀ - volume of gross national product of the basic period in the current prices of the basic period, GDP₁ - volume of gross national product of the current period in real terms.

I.e. the parameter of an index of physical volume of gross national product characterizes changes of physical volume of made production (the goods and services). Knowing GDP₀ and I_p.v.GDP , it is possible to calculate new value GDP₁. Therefore the task of forecasting of gross domestic product can be reduced to forecasting dynamics.

Basis of a forecasting model are neural networks which represent the new and rather perspective computing technology, giving new approaches to research of dynamic tasks in financial area.

As initial data for the decision of this task the following are considered:

1. gross domestic product on quarters,
2. an index of physical volume of gross domestic product,GDP deflator,
3. a consumer price index,
4. number of the employed population,
5. an aggregate number of unemployeds,
6. pure export of goods and services,
7. taxes,
8. deductions on social insurance,
9. volume of investments,
10. charges on final consumption of house facilities,
11. the governmental charges,
12. monthly average minimal wages.

Mathematical statement of a task: values of multivariate time discrete function F on an interval {1, M} are given. Since all attributes depend on time, we shall present F(X₁ ,..., X₁₃) as F(t) - function of time. It is required to calculate during the moment of time n predicted values of function F on a time interval {n+1, n+α}. In figure below grey color known values of function F, i.e. value of function on an interval {1, M} are designated. Here n - a present situation of time; {n+1, n+α} - a time interval for which it is required to calculate predicted values of function F; and {n-T+1, n} - a time interval, values of function and value of its variables on which at present time move on an input of a neural network. In each moment of time n ε {T,...,M-α} is formed an element of training sample in which an entrance signal of a neural network is the vector of values of function F and its variables on an interval {n-T+1, n}, and a desirable target signal is the vector of values of function F on an interval {n+1, n+α}. Thus, amount of training vectors equally M-T-α .

Algorithm of the decision of a task:

1. definition of optimum amount of factors (initial data) k . Since it is possible to expand the list of initial data presented above other parameters, it is necessary to find a way to group entrance data on semantic similarity, having found, thus, a small number of independent parameters for the description of a researched parameter of GDP. Reduction of dimension at transition from the big set of factors to much smaller list more essential will help to remove duplication of the information, having excluded little informative or "rustling" variables. For performance of this requirement use of the factorial analysis which purpose consists in an explanation intercorrelation between observable variables the minimal number of directly not observable reasons - factors is possible;

2. definition of optimum dimension of a vector of entrance data T. Dimension of a vector of entrance data can be chosen multiple to length of one of basis cycles of some. It can improve training a neural network since at definition of the optimum size of a vector of entrance data by experiments significant computing expenses are required, and the uniform theory about an optimality of the sizes of an entrance window does not exist.