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To receive news and publication updates for The Scientific World Journal, enter your email address in the box below. This is an open access article distributed under the Forex predictions 2016 Commons Attribution Licensewhich permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper deals with application of quantitative soft computing prediction models into financial area as reliable and accurate prediction models can be very helpful in management decision-making process.

The authors suggest a new hybrid neural network which is a combination of the standard RBF neural network, a genetic algorithm, and a moving average. The moving average is supposed to enhance the outputs of the network using the error part of the original neural network.

To determine the forecasting efficiency, they perform a comparative statistical out-of-sample analysis of the tested model with autoregressive models and the standard neural forex predictions 2016. They also incorporate genetic algorithm as an optimizing technique for adapting parameters of ANN which is then compared with standard backpropagation and backpropagation combined with -means forex predictions 2016 algorithm. Finally, the authors find out that their suggested forex predictions 2016 neural network is able to produce more accurate forecasts than the standard models and can be helpful in forex predictions 2016 the risk of making the bad decision in decision-making process.

Techniques of artificial intelligence and machine learning started to apply in time series forecasting. One of the reasons was the study of Bollerslev [ 1 ], where he proved the existence of nonlinearity in financial data. First models of machine learning applied into time series forecasting were artificial neural networks ANNs [ 2 ]. This was due to the fact that the artificial neural network is a universal functional black-box approximator of nonlinear type [ 3 — 5 ] that is especially helpful in modeling of nonlinear processes having a priori unknown functional relations or system of relations is very complex to describe [ 6 ] and they are even able to model chaotic time series [ 7 ].

They can be used for nonlinear modeling without knowing the forex predictions 2016 between input and output variables. Thanks forex predictions 2016 this, ANNs have been widely used to perform tasks like pattern recognition, classification, or financial predictions [ 8 — 11 ]. Following the theoretical knowledge of perceptron neural network published by McCulloch and Pitts [ 12 ] and Minsky and Papert [ 13 ], nowadays, it is mainly radial basis function RBF network [ 1415 ] that has been used as it showed to be better approximator than the basic perceptron network [ 16 — 18 ].

We chose the RBF neural network for our exchange rates forecasting experiment because according to some studies [ 19 ] ANNs have the biggest potential in predicting financial time series. In addition, Hill et al. As, according to some scientists [ 21 ], the use of technical analysis forex predictions 2016 can lead to efficient profitability on the market, we decided to combine our customized RBF network with moving averages [ 22 ].

We will use the simple moving average to model the error part of the RBF network as we supposed it could enhance the prediction outputs of the model. Applying the prediction analysis, the forecasting ability of this nonlinear model will be compared and contrasted with a standard neural network and an autoregressive AR model with Forex predictions 2016 errors to determine the best model parameters for this currency pair forecasting problem.

We will provide out-of-sample evidence since it focuses directly on predictability as it is forex predictions 2016 to avoid in-sample overfitting for this type of nonlinear models [ 23 ].

The soft computing application we suggest is novel in two ways; we use the standard neural network hybridized with simple forex predictions 2016 averages to form a whole new hybrid model.

Except for the standard algorithm for training the neural network, we also use other advanced technicques. Hybrid models have become popular in the field of financial forecasting in recent years. Since studies from Yang [ 24 ] or Clemen [ 25 ] theoretically proved that a combination of multiple models can produce better results, we will also forex predictions 2016 the combined model of customized RBF neural forex predictions 2016 supplemented by genetic algorithms for weights adaptation and simple moving average tool for modeling the error part of the RBF.

We eliminate the error of the neural network by modeling the residuals of RBF. Let be a function defined as F: Let be a restriction of defined aswhere is a complement of to. The necessary condition is that the model must be adapted to approximate the unknown function ; that is, the model must fulfill the condition that the difference between estimated output produced by the model and the original value is minimal.

The input vector forms the input layer of the network; are weights going from the input layer to the hidden layer that is formed by hidden forex predictions 2016.

In the RBF network, the radial basis function of Gaussian type instead of forex predictions 2016 sigmoid function is used for activating neurons in hidden layer of a perceptron network.

The Gaussian function for activating neurons is for th hidden neuron defined as, where is the variance of th neuron and is the potential of the neuron. Furthermore,are weights between th hidden neuron and the output layer that is represented by just one neuron the network output. Activated neurons are weighted by weight vector in order to get the output of the network counted as. The neural forex predictions 2016 we used for this research was RBF which is one of the most frequently used networks for regression.

RBF has been widely used to capture a variety of nonlinear patterns see [ 26 ] thanks to their universal approximation properties see [ 27 ]. In order to optimize the forex predictions 2016 of the network and to maximize the accuracy of the forecasts we had to optimize parameters of ANN.

The most popular method for learning in multilayer networks is called backpropagation. It was first invented by Bryson and Ho [ 28 ]. But there are some drawbacks to backpropagation. Furthermore, the convergence of this algorithm is slow and it generally converges to any local minimum on the error surface, since stochastic gradient descent exists on a surface which is not flat. So the gradient method does not guarantee to find optimal values of parameters and imprisonment in local minimum is forex predictions 2016 possible.

As genetic algorithms have become a popular optimization tool in various areas, in our implementation of Forex predictions 2016, backpropagation will be substituted by the GA as an alternative learning technique in the process of weights adaptation. Genetic algorithms GAwhich are EC algorithms for optimization and machine learning, are stochastic search techniques that guide a population of solutions towards an optimum using the principles of evolution and natural genetics [ 30 ].

Adopted from biological systems, genetic algorithms are based loosely on several features of biological evolution [ 31 ]. In order to forex predictions 2016 properly, they require five components [ 32 ], that is, a way of encoding solutions to the problem on chromosomes, an evaluation function which forex predictions 2016 a rating for each chromosome given to it, a way of initializing the population forex predictions 2016 chromosomes, operators that may be applied to parents when they reproduce to alter their genetic composition, parameter settings for the algorithm, the operators, and so forth.

GA are also characterized by basic genetic operators which include reproduction, crossover, and mutation [ 33 ]. Given these genetic operators and five components stated above, a genetic algorithm operates according to the following steps stated in [ 29 ]. When the components of the GA are chosen appropriately, the reproduction process will continually generate better children from good parents; the algorithm can produce populations of better and better individuals, converging finally on results close to a global optimum.

Additionally, GA can efficiently search large and complex i. Also, GA should not have the same problem with scaling as backpropagation. One reason for this is that it generally improves the current best candidate monotonically. It does this by keeping the current best individual as part of their population while they search for better candidates.

In addition, as Kohonen [ 34 ] demonstrated that nonhierarchical clustering algorithms used with artificial neural networks can cause better results of ANN, unsupervised learning technique will be used together with RBF in order to find out whether this combination can produce the effective improvement of this network in the domain of financial time series.

We will combine Forex predictions 2016 with the standard unsupervised forex predictions 2016 called -means see [ 35 ]. The most forex predictions 2016 type of characteristic function is location clustering.

And the most common distance function is Euclidean. The -means will be used in the phase of nonrandom initialization of weight vector performed before the phase of network learning. In many cases it is not necessary to interpolate the output value by radial functions, it is quite sufficient to use one function for a set of data clusterwhose center is considered to be a center of activation function of a neuron.

The values of centroids will be used as initialization values of weight vector. Weights should be located near the global minimum of the error function 1 and the lower number of epochs is supposed to be used for network training. The reason why we decided to use -means is that it is quite simple to implement and in addition to that, in the domain of nonextreme values, it is relatively efficient algorithm.

In our experiments, the adaptive version of -means will be used which is defined as follows: We chose forex market for our experiments. Due to validation of a model, data were divided into two parts Figure 7. These observations include new data which have not been incorporated into model estimation parameters of the model were not changing anymore in this phase.

The reason for this procedure is the fact that an ANN can become so specialized for the training set that loses forex predictions 2016, hence the accuracy in the test set. We used our own application of RBF neural network implemented in JAVA with one hidden layer according to Cybenko [ 36 ]; the feedforward network with one forex predictions 2016 layer is able to approximate forex predictions 2016 continuous function.

For the hidden layer, the radial basis function was used as an activation function as it has been showed that it provides better accuracy than the perceptron network. We estimated part of the RBF model with several adapting algorithms: RBF implemented with a backpropagation algorithm, a genetic algorithm, and combination of -means and backpropagation.

As for the backpropagation learning, the learning rate was set to 0. The number of epochs for each experiment with backpropagation was set to as this showed to be a good number for backpropagation convergence. The final results were taken from the best of epochs and not from the last epoch forex predictions 2016 order to avoid overfitting of the neural network. Coordinances of clusters were initiated as coordinances of randomly chosen input vector.

The number of clusters was set to the number of hidden neurons. For GA algorithm the following was needed: Our implementation of the genetic algorithm we used for weight adaptation is as follows. The chromosome length was set according to the formula: A specific gene of a chromosome was a float value and represented a specific weight in the neural network.

The whole chromosome represented weights of the whole neural network. Forex predictions 2016 fitting function for evaluating the chromosomes was the forex predictions 2016 square error function MSE. The chromosome individual with the best MSE was automatically transferred into the next generation. The other individuals of the forex predictions 2016 generation were chosen as follows: The fittest of them was then chosen as forex predictions 2016 parent.

The second parent was chosen in the same way. Forex predictions 2016 new individual was then forex predictions 2016 by crossover operation. Otherwise, the new individual received the weight of the second parent. The mutation rate was set to 0. If performed, the specific gene weight of a chromosome was changed to a random value.

The size of the population and the number of generations for the genetic algorithm were set accordingly to the settings of backpropagation. Based on some experiments, we used the size of the population forex predictions 2016 equaled and the number of generations was set to When the best configuration of the RBF network was found, the RBF error was then forex predictions 2016 in order to minimize the total error of the model.

Using moving average, the forecast of the future error of the RBF was counted as an average of last forex predictions 2016 errors. We used only simple moving average: To find out the optimal number of the parameters of moving average tool, we used various numbers of previous errors for counting the future average value of RBF error.

The numerical characteristic for assessing models called mean squared error MSE was used: In order to make a comparison with standard statistical models, we also performed the empirical Box-Jenkins analysis [ 37 ] in order forex predictions 2016 compare our suggested model with standard statistical model for details of Box-Jenkins analysis see the appendix. The data, as stated above, was downloaded from the following website:

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