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

Tambov State University named after G.R. Derzhavin

Forecasting the currency exchange rates using technical analysis and artificial neural networks

As we know the currency exchange rates system condition is characterized by time series . For simulating the time series it is necessary to discover the 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 [1].

Artificial neural networks (ANN) are actively used by institutional investors which work with a large amount of information and which need to make allowances one currency to other. The difference to technical analysis is the possibility to find optimal factors 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 and technical analysis. It needs to train 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].

If technical analysis is used, then the time series of quotations usually is broken into intervals. First and last values of each interval are the open cost () and close cost () and the highest () and the lowest () within each interval are defined.

The most popular tool of technical analysis is the moving average (MA) which calculates the mean value of cost in a strict time interval. So this tool is method of smoothing of cost factors which are cumulated for several periods. The MA can be calculated for each serial data array such as open and close cost, maximum and minimum quotations, trade size or value of other indicators (for example MA itself).

There are several kinds of MA:

· simple MA ;

· exponential MA ;

· smoothed MA ;

Here , are costs of open and close in time moment , m is the length of smoothing period, is cost participate coefficient.

An other used tool is a stochastic oscillator which builds two series. The first series values are calculated by formula

	(1)

and the second is the MA of first. Often a third series is added which is MA of the second. The crossing of smoothed and non-smoothed means changes the direction of the moment of the quotations. It the smoothed curve crosses the non-smoothed curve from below means growing start and othersize from above means growing end [5].

There are different strategies of using the MA and the stochastic oscillator approach.

Best results of forecasting of currency pair €/$ (Euro and US dollar) were got using a stochastic oscillator with periods 5, 3 and 3. Quotations values were calculated correctly with a probability of 0.65.

We will use two ANN models. First of these it a multilayer perceptron (MLP) which is a structure in which each neuron in each layer (except output layer) is connected to all neurons of the next layer. Weight coefficients is are calculated by formula where N_L is layers count, is the number of neurons in i-th layer [1]. The second structure is a Volterra network which is a dynamic network for the nonlinear adaptation of array of signals belated for each other. The vector from equation activates the network at moment m. This polynomial degree is called the Volterra series degree [2].

The testing consists of several steps:

· the algorithm starts at time t=t₀, and sets the test index to k=0;

· the pattern is formed;

· weight coefficients are trained by a gradient algorithm of steepest descent [3];

· the input vector is formed and the ANN calculates the output output value y_N+1 ;

· the quotation change is calculated and used for calculation of value

· the time t is changed (t = t + c) and the test index is incremented (k = k + 1);

· the algorithm goes to step 2.

These tests show the probability of obtaining the correct direction of the quotation change. For multilayer perceptron it is 72% and for a Volterra network it is 76%. The technical analysis allows to forecast the direction of change with probability value of about 65%. So the neural network analysis using a Volterra network is efficient.

Figure 1 shows series of currency pair quotations, both empirical and forecast ( by the multilayer perceptron and the Volterra network).

It follows from the experimented results that a Volterra ANN with four layers and twelve inputs allows to predict the correct direction of the quotation change with a probability of 76%. So such a structure can be used for forecasting of exchange rates.

Pic. 1. Empirical exchange rates, exchange rates forecast by multilayer perceptron and by Volterra.

(1)

Literature

1. Кузнецов С.П. Динамический хаос. // Москва, 1994. – 274 с.

2. Бэстенс Д.Э. ван ден Берг В.М. Вуд Д. Нейронные сети и финансовые рынки: принятие решений в торговых операциях. // Москва: ТВЦ. 1997. – 236 с.

3. Вострокнутова. А.И. Модели прогнозирования курсов акций российских нефтяных компаний // Извесия Санкт-Петербургского университета экономики и финансов. \textnumero3), СПб. 2000. – C. 126-144.

4. Зенкова Н.А. Моделирование на основе аппарата искусственных нейронных сетей как метод исследования в психологической науке. // Вестн. Тамб. ун-та. Сер. Естеств. и техн. науки. Тамбов: 2009. Т. 14, Вып. 3. – С. 577-591.

5. Osowsky S. Sieci neuronowe w ujeciu algorytmicznym // Warszawa. 1996.

6. Kryuchin O.V., Arzamastsev A.A., Troitzsch K.G. The prediction of currency exchange rates using artificial neural networks [Электронный ресурс] — Электрон. дан. // Arbeitsberichte aus dem Fachbereich Informatik Nr. 4/2011. Koblenz. 2011. 12 p. — http://www.uni-koblenz.de/%7Efb4reports/2011/2011_04_Arbeitsberichte.pdf