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Deal 2010 DealListopad Marzec 2010

BADANIE NAUKOWE

ral network, by which is meant that the data used for training and testing the network is paired with the desired response of the network, the target. Knowledge of the desired response provides a starting point for iteratively modifying the network, by comparing the observed response with the target and using the error to drive the network’s free parameters in a direction that will minimize the error for repeated presentations of the training input data. This is the essence of the backpropagation method, which backpropagates the error through the network, adjusting the weights, which are the free, modifiable parameters. There are many commercially available neural network programs designed for use on financial markets and there had been some noticeable reports of their successful application. However, like other computer program, neural networks are only as good as the data given and the questions that are asked of the proper use of a neural network, artificial intelligence, involves spending time understanding and cleaning data: removing errors, preprocessing and postprocessing. RESEARCH The analysis of market prices with a view to forecasting future behaviour presumes that such an approach is meaningful, whether its methodology is technical analysis (which assumes historical price studies alone are

Figure 4. KGHM’s neural network structure

Source: Authors realisation

ver nonlinear relationships in input data makes them ideal for modeling nonlinear dynamic systems such as the stock market. However, there are various neural network configurations to model the stock market. This study is build upon the Multilayer - perceptrons (MLPs) model with backpropagation, used in NeuroSolution.4 computer program. The first step in designing any neural network is to collect training data. The designer needs to decide what he

Figure 3. Fragment of a data set date

opening price (pln)

maximum price (pln)

minimum price (pln)

closing price (pln)

17.02.2010 18.02.2010

94.80

95.40

94.20

94.80

96.40

94.05

19.02.2010

93.80

96.25

22.02.2010

97.75

97.80

23.02.2010

96.60

97.10

24.02.2010

94.05

25.02.2010

94.00

output

error

95.00

95.730736

-0.730736

94.75

96.336213

-1.586243

93.20

96.00

96.336213

-0.336243

96.40

96.60

95.730736

0.869264

94.50

94.60

95.730736

-1.130736

94.80

92.85

94.00

95.160172

-1.160172

95.85

91.60

92.10

96.336213

-4.236243 -0.573572

26.02.2010

95.00

96.40

94.30

96.40

96.973572

01.03.2010

98.10

99.90

97.40

98.30

97.302826

0.997174

02.03.2010

98.80

100.10

97.60

99.80

97.979037

1.820943

03.03.2010

99.80

101.80

98,95

101.00

97.638245

3.361755

04.03.2010

99.80

102.40

99.40

100.10

97.979057

2.120943

05.03.2010

100.00

102.20

99.95

101.50

98.324402

3.175558

08.03.2010

101.10

102.50

100.40

102.00

97.989037

4.020943

Source: Authors calculations

sufficient for prediction) or fundamental analysis (which studies general economic variables, company performance statistics, prevailing supply and demand etc.) The purpose of this part of atricle is to predict the KGHMs closing prices using neural network. As described previously, it is a computer program or hardwired machine that is designed to learn in a manner similar to the human brain. Their ability to disco-

wants the neural network to do and what data requirements are needed to train the network. Will it be a classifier, an estimator (modeler) or a self-organizer? It must be determined what the neural network will output in response to the data used as the network input. What is more, we needed to make sure that data-collection process is repeatable and decide how big amount of data should be included. A larger number of samples generally give the network a bet-

ter representation of the desired problem and increase the likelihood that the neural network will produce the desired outputs. Following study had been build upon over 100 daily (opening, maximum, minimum and closing) KGHMs share prices in The Warsaw Stock Exchange (WIG20 index). In next phase is choosing a methodology. Backpropagation is a form of data learning (supervised) where every input vector has an adaptive parameter which is changed according to prespecified procedure. Moreover, in our analysis there was used a highly recommended method for stopping network training - cross validation, which monitors the error on an independent set of data and stops training when this error begins to increase. This is considered to be the point of best generalization. CONCLUSION It is difficult to identify good raw data, preprocessing this data, training a network and repeating this process until a good model is developed. However, the neural networks, if properly trained, do have the capability to forecast financial markets and the individual investor could benefit from the use of this forecasting tool. Although neural networks are not perfect in their prediction, they outperform all other methods and provide hope that one day we can more fully understand dynamic, chaotic systems such as the stock market.

Małgorzata Kozak malgorzata.kozak@skninwestor.com Joanna Syczewska joanna.syczewska@skninwestor.com

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