The paper discusses methods for forecasting financial markets. Their advantages and disadvantages are presented. A genetic approach for the formation of the structure and training of the neural network is proposed. The method of forming a neural network based on a genetic algorithm is given.The effectiveness of the proposed methodology is presented as a result of the task of forecasting the stock market.
In this situation, neural networks (NN) can serve as an adequate apparatus for solving problems of diagnostics and forecasting, and, as very promising, radial base structures, characterized by high learning speed and universal approximating capabilities, should be noted.
The aim of the work is to develop a methodology for the formation of neural networks for the financial market analysis.
For forecasting systems based on NN, a heterogeneous network consisting of hidden layers with a non-linear
activation function of neural elements and an output linear neuron shows the best quality. The disadvantage of most
nonlinear activation functions is that their output values are limited by the [
Various network learning algorithms and their modifications are used for the network training [
Training in the method of back propagation of an error is reduced to the selection of the values of the forwarddirected neural network weights, based on the principles of the fastest descent. One of the main drawbacks of this classic algorithm is the possible hit in the local minima of the cost function.
The analysis of multilayer neural networks and their learning algorithms revealed a number of shortcomings
and emerging problems [
4. The impossibility of determining the local and global minimum points, since the gradient method does not distinguish them;
5. The effect of random initialization of NN weighting factors on the search for the minimum of the root-meansquare error function.
An alternative to the method of back propagation of errors can serve as genetic algorithms. Genetic algorithms
are used to solve optimization problems using the evolution method, i.e. by selecting the most appropriate one from a
variety of solutions. They differ from traditional optimization methods in the following properties [
The purpose of the training is to minimize the cost function E(n)=(ek2(n))/2, where ek(n) = dk(n) – yk(n) is the error, dk(n) is the desired output of the neural network, yk(n) is the real output of the neural network, n is the iteration number.
The parameters of the problem are the weights that determine the point of the search space and, therefore, represent a possible solution.
If the weights take real values from the interval [
If it is required to find a solution with accuracy up to q=2 significant decimal figures for each weight, then the interval [a, b] should be divided into (b – a)·10q identical subintervals. This means applying discretization in increments of r=10-q The smallest positive integer mi satisfying the inequality (b – a)·10q ≤ 2m–1 determines the necessary and sufficient length of the binary sequence required to encode a number from an interval [a, b] in increments of r. As a result, the length of the binary coding sequence is 8 bits.
When coding real numbers, an integer is taken as the value of the gene that determines the number of the interval (The Gray code is used). As the phenotype value, the number that is the middle of this interval is taken.
The initial chromosome population is randomly assigned. When calculating the neural network output values, you can use the logistic activation function with the learning speed parameter η=1.
The stage of selection of parental chromosomes for creating a new population performs the greatest role in the successful functioning of the algorithm. The most effective is the tournament method. The essence of the method is as follows. All individuals of the population are divided into subgroups of 2-3 individuals each. The choice of parents is made randomly with a probability less than 1.
In the classical genetic algorithm, two main genetic operators are used: the crossover operator and the mutation operator. The probability of crossing is large enough (usually 0,5≤ pc≤1), the probability of mutation is established very small (most often 0≤ pm≤0,1). This means that interbreeding in the classical algorithm is almost always performed, while mutation is quite rare.
The crossover operator acts as follows:
from the population with probability pc two individuals are selected, which are included in the composition of the temporary parent population; the point of crossing lk is determined (also randomly); the concatenation of the part of the first and second parents.
The mutation operator with probability pm changes the value of a gene in the chromosome to the opposite. The
probability of mutation can be calculated by randomly choosing a number from the interval [
The chromosomes obtained by applying genetic operators to the chromosomes of the temporary parent population are included in the new population. It becomes the current population for this iteration of the genetic algorithm. At each iteration the value of the fitness function for all chromosomes of this population is calculated, after which the condition of the algorithm stop is checked. As such a condition, either a restriction on the maximum number of epochs of the algorithm functioning is applied, or the algorithm convergence is determined by comparing the population's fitness function values at several epochs. When this parameter is stabilized, the algorithm stops.
The genetic algorithm was used in the study of neural network structures to forecast the stock prices of public JSC (joint-stock company) “Lukoil”.
The studies were conducted for the 2017-year time series. Fig. 1, 2 shows the results of the search for optimal neural networks. Studies were conducted for MLP type networks (three and four-layer network). It is known that the search for the type of neural network and structure is a rather time-consuming procedure, so the intermediate task of determining the initial “prototype” was solved, after which it was determined that the further structure of the NN was further refined.
The results of calculations showed that for the stock price of JSC “Lukoil” the optimal structures are neural networks with the following indicators: type –MLP; three-layer structure: 3 input neurons – 8 neurons of the hidden layer – 1 output neuron (Fig. 2), or MLP; three-layer structure: 1 input neuron – 11 neurons of the hidden layer – 1 output neuron (Fig. 1).
Conclusions. The neural network structures obtained were used to forecast the value of LUKOIL stocks (Fig. 3, 4).
The forecasting accuracy was 73% for LUKOIL stocks, which is a high result and exceeds the forecasting results by other methods.
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In the future, the forecast results can be used in the management of project-oriented organizations [