P.h.D. Kryuchin O.V., Kryuchina E.I.

Tambov State University named after G.R. Derzhavin

The currency exchange rates prediction and artificial neural networks

The prediction of financial time series is an actual problem of economics because changing cost of shares and currency exchange rates influences different economic parameters. For a long time it is assumed that financial time series are random but in the 1980s the theory of deterministic chaos appeared. This theory predict that there are many hidden conformities in financial time series.

The deterministic chaos theory suggests that a financial time series is a dynamic system. There is a group of parameters for such a system which characterizes the system condition and allows to calculate system values at every point of time from initial values by special convention (is defined by the following function of system evolution ) [1]. Here is group of parameters characterize system condition, L is lag space size (number of previous series values used to calculate the value of the current value), are manager parameters, is the system evolution function. The currency exchange rates system condition is characterized by time series . Here is currency exchange rates at time . For simulating the time series it is necessary to discover the function and the parameter from function . The flavor of function is unknown so in simulation this function is changed to approximate function F which is defined for minimum difference between empirical currency and forecast currency in equation . Here c is discharging coefficient which defines the length of the forecasting period. So the target of forecasting currency exchange rates is to detect the parameters F, L and c by minimizing the value .

One of the most often used strategies is direction detecting. So at the current time it detects the next direction of change and calculates value at time . This calculated value is . Then the difference of the values at points and is compared to swap value . The swap value is point around radius in which all operations are unprofitable. If constraint is executed then the operation will be open. If new value is greater than current value then a buying operation is recommended othersize a selling operation. So it is necessary to define one of three conditions:

To solve this task it is possible to use different methods, for example technical or neural network analysis. This analysis has not limitation of the character of the input information. This may be a time series or information about behavior other market factors. For example, artificial neural networks (ANN) are actively used by institutional investors (such as large pension funds etc.) which work with a large amount of information and which need to make allowances one currency to other. The difference to technical analysis (based on general recommendations) is the possibility to find optimal factors (for currency pair quotations forecasting) and to use them in forecasting [2-3].

The aim of this paper is to predict exchange rates between Euro and US dollar using an artificial neural network. To achieve this aim, several tasks have to be solved. These tasks are the training of ANN structure witch consider time series of currency pair €/$ quotations, the check of ANN-model adequacy based on this structure, the forecasting result of technical and neural networks analysis comparison and to formulate a corollary about the possibility to use ANN for predication.

ANNs are mathematical instruments which are computer models of biological neural networks, which can be trained using log-normal observations and can be used with information dearth or its noisiness. This instrument is very flexible and this property allows to consider different log-normal red observations using the change of structure and of manager parameters of model [4].

Training ANNs is reduced to minimizing the inaccuracy function . Here are weight coefficients.

The ANN which simulates currency pair quotations series are formulated using the algorithm defined in [5]:

· The lag space size L is searched. This value defines the number of input neurons in the ANN. Usually this value lies in the band (8; 16) [6].

· The type of structure of ANN is selected. The numbers of neurons in hidden layers and the number of hidden layers are defines by the configuration of the structure.

· The value of the number of the discharging.

· The optimal number of pattern lines count are calculated. This value is defined by the structure size and the number of weighs. If there are N quotations then the number of pattern lines is N-L [7].

· For pattern building the quotation values at time points are calculated. These values are .

· The input pattern (X) and output pattern (D) are formulated

· Weight coefficients are changed using a gradient algorithm of the steepest descent [8].

There are not monosemantic methods of searching of the lag space and the discharging values searching because each method has advantages and disadvantages. For the exchange rates used in this paper €/$ witch series are showed in picture 1 it sets parameter L whose time series is show in figure 1, and c taken the values 15, 30, 60 and 120 minutes (standard periods witch used in trade strategies).

Pic. 1. Quotations of currency pair.

Pic. 2. Quotations of currency pair (real and predicating).

Literature

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