Abstract: In this study, it is aimed to illustrate that Artificial Neural Network (ANN) can be used for predicting the stock price behaviour in terms of its direction. Financial daily statistical data, derived from raw price data obtained from Istanbul Stock Exchange (ISE), which is the only stock market in Turkey, have been defined in terms of five independent variables that are grouped in seven different Prediction System (PS) models to which eight different ANN and Logistic Regression (LR) models have been applied. For this purpose, a software library package is developed using C#.NET to run the ANN models whereas a commercial statistical analysis software package is used to run the LR model. At the end of the study; the best PS and ANN models are determined for ANN methodology by comparing the average mean squared errors of training sets and the best PS model is determined for LR methodology by eliminating the insignificant independent variables; the outputs of the developed software library package and a commercial ANN software are compared on the basis of prediction success rate and the accuracies of prediction by ANN and LR methodologies are compared on the basis of coefficient of determination. The results show that; the best results are obtained for the PS model that has used stochastic indicator for 14 days (K14%), stochastic moving average (D3%) and relative strength index of 14 days (RSI14) simultaneously for both ANN and LR methodologies whereas the best ANN model has consisted of three inputs, 11 hidden neurons in single hidden layer and one output; developed software library package performs statistically same as the commercial software; statistically ANN methodology outperforms LR methodology; and there is relevant empirical evidence that ISE-30 is not weak form efficient.
INTRODUCTION
Stock price behavior has been a widely questioned and not a mutually agreed area of researchers, where the main question is whether stock price behaviors are predictable or not.
Researchers, who believe that stock prices do not follow a trend, act in a random walk and cannot be predicted, are usually followers of a hypothesis called the Efficient Market Hypothesis (EMH). EMH has been a widely accepted theory which claims that the prices are defined in a random walk procedure, making price behavior completely unpredictable. It also suggests that it is not possible for any kind of prediction algorithm to outperform a buy and hold strategy (a long term trading strategy based on the concept that in the long run financial markets give a good rate of return) consistently for a long period of time. This hypothesis has been discussed, expanded and deepened by Reilly and Brown (1997), Dutt and Ghosh (1999) and Dietrich et al. (2001).
As oppose to EMH, various studies have been done using different methodologies and different indicators to predict stock price behaviour. According to Hellstrom and Holmstrom (1997), there are four main methodologies to predict stock market; fundamental analysis, technical analysis, time series forecasting and machine learning. As indicators of stock price behaviour, different combinations of various indicators such as; closing stock price, stock market index value, foreign exchange rate, interest rate value, vector curve, turnover, moving average, momentum, relative strength index, stochastic and moving average of stochastic have been used in previous researches (Kimoto et al., 1990; Tsibouris and Zeidenberg, 1995; Yao and Poh, 1995; Fernandez-Rodriguez et al., 2000; Egeli et al., 2003).
In recent studies, Artificial Neural Network (ANN), which is the most popular machine learning methodology, with various sets of indicators as inputs and with various topologies, has been utilized for stock price behaviour prediction and contradictory to EMH, has shown that stock price behaviour can be predicted and ANN approach can outperform conventional methods (Van Eyden, 1996; Yao and Poh, 1995; Fernandez-Rodriguez et al., 2000; Phua et al., 2000; Egeli et al., 2003; Versace et al., 2004; Yümlü et al., 2004).
The main objective of this study is to show that, with a well chosen set of indicators and ANN topology, ANN method has the capability to predict stock price direction and in this context, outperforms the conventional technique, Logistic Regression (LR).
MATERIALS AND METHODS
Stock price direction, as stated before, is mostly predicted by financial indicators and the act of selecting the true indicators, in other words designing a correct Prediction System (PS) model, is not easy and varies from market to market and even stock to stock. Based on the previous studies discussed before and the opinions of the experts, the following financial indicators are chosen to be the indicators of the PS models in this study:
| • | Moving average of 14 days (MA14) |
| • | Moving average of 37 days (MA37) |
| • | Stochastic indicator for 14 days (%K14) |
| • | Stochastic moving average (%D3) |
| • | Relative strength index of 14 days (RSI14) |
Considering these indicators, seven different PS models (PSM1 to PSM7) consisting of different sets of these indicators have been considered for the prediction of stock price direction:
Thus, the effectiveness of different combinations of financial data has been investigated for the stock price direction prediction.
Istanbul Stock Exchange (ISE-30) have been chosen for the data set of
this study. Daily closing prices of each stock in ISE-30 for each day
have been acquired from a private data feeder company and these prices
are then used to calculate the indicators of the PS models. Statistical
summary of this data is given in Table 1.
| Table 1: | Statistical summary of the data set |
Average number of days for available data of the stocks is 2255. Since number of available trading dates for stocks listed under the name of DENIZ, DOAS and VAKBN are less than 50% of the average number of days; they are not included in this study due to insufficient amount of data, thus, the number of stocks used in this study is dropped to 27.
The period used in the training data sets are between January 5, 1998 (first trading date of 1998) and December 29, 2005 (last trading date of 2005). The period used in the testing data sets are between January 6, 2006 (first trading date of 2006) and August 31, 2007 (last trading date of available data).
As suggested and used in previous studies (Kimoto et al., 1990; Freisleben, 1992; Azoff, 1994; Zekic, 1998; Gencay, 1998; Quah and Srinivasan, 1999; Fernandez-Rodriguez et al., 2000; Man-Chung et al., 2000; Egeli et al., 2003; Heaton, 2005), backpropagation ANN model with one hidden layer with eight possible different numbers of neurons for the hidden layer, thus, eight different ANN models have been prepared for seven different PS models. The number of inputs of the ANN models is set to be the number of indicators of the corresponding PS model and the stock price direction, within the boundary values 0 to 1, is set to be the output that follows the below rule:
| • | Goes down if output is greater than or equal to 0.0 and less than 0.5 |
| • | Stays same if output is equal to 0.5 |
| • | Goes up if output is greater than 0.5 and equal or less than 0.0 |
For all of the ANN models, the following network parameters are taken the same:
| • | Learning rule: Momentum (Momentum factor = 0.5) |
| • | Stopping criteria: 10,000 cycles |
| • | Learning rate: 0.2 |
| Fig. 1: | Class diagram of the developed software library package |
| • | Activation function: Linear Sigmoid |
| • | Initial weight: Randomized |
For applying the ANN models to PS models a software library package is developed by object oriented methodology using C#.NET that can easily be integrated to other systems, such as trading applications. The class diagram of the developed software library package is given in Fig. 1.
Using the developed software package library, eight different ANN models are applied to each of the seven PS models for each stock included in ISE-30. Due to the rules that do not yield a possible combination of number of inputs of the PS model with the number of neurons in the hidden layer of the corresponding ANN model, 26 combinations of ANN versus PS models are dropped from the study thus leaving 30 combinations. For each of these 30 combinations, averages of the mean squared errors of training of 27 different stocks are calculated. The ANN and PS models that correspond to the smallest average mean squared error of the trainings are selected to be models of the study and for each of the 27 stocks, the predicting ability of the developed software library package is tested by comparing the predicted outputs of the selected models with actual data.
To check the reliability of the developed software library package, a commercial ANN software is run for the selected ANN and PS models and the outputs are statistically compared with the outputs of the developed software library package.
ANN outputs can also be compared with the results of statistical methods, generally regressive models (White, 1988; Weigend et al., 1990; Bernd and Klaus, 1996; Dutta and Shekbar, 1988; Chiang et al., 1996). Models which are used in these studies are targeted on forecasting a future stock or index value. Since this study focuses on predicting stock price direction, which is represented by a binary number, a regressive model with a binary output is appropriate for comparison of the outcomes. LR methodology is a statistical method used when the dependent variable is desired to be interpreted as binary (Dreiseitl and Ohno-Machado, 2002), therefore it is an efficient way to measure the accuracy and performance of ANN model when the output is going to be classified as binary (Bell et al., 1990; Huang et al., 1994; Schumacher et al., 1996; Luther, 1998; Dreiseitl and Ohno- Machado, 2002). In this study, the outcomes of ANN approach are compared with the outputs of LR method. For that purpose, the five financial indicators chosen before are used as independent variables and the stock price direction is used as the dependent variable in LR methodology. A commercial statistical analysis software package is used for running up the LR method and the best PS model is determined by taking the significant independent variables into consideration whereas correctness and correlation factors are used for the comparison of outputs of the ANN and LR methodologies statistically.
RESULTS AND DISCUSSION
After applying the ANN models to each system model for 27 stocks included in ISE-30 using the developed software library package, ANN model with three inputs, 11 hidden neurons in the single hidden layer and one output (ANNM.3.11.1) applied to the PS model with the three indicators, R14, K14 and D3 (PSM5) gives the lowest average mean squared error of training. Therefore, these models are selected to be the models of this study. Table 2 gives the success rates of the predicted outputs (price goes down-price stays same-price goes up) of the application of ANNM3.11.1 to PSM5 for 27 different stocks in comparison to the actual price direction data. Average of the success rates is 78.47% and for every stock, the success rate is consistently much higher than 50-50 chance indicating a high predicting capability of the models.
The reliability of the developed software library package is checked by applying the same selected models (ANNM3.11.1-PSM5) to 27 stocks using a commercial ANN software. Table 3 gives the correlations between the predicted outputs and the actual price direction data for the results of both the developed software library package and commercial ANN software. One tailed t-test applied to these correlations shows that in the 95% confidence interval, there is statistically no significant difference (p = 0.48) between these sets indicating that the developed software library package is reliable as much as the commercial ANN software.
The results of ANN approach are also compared with the outcomes of the
LR method to test if ANN approach outperforms LR method. A commercial
statistical analysis software is used to run the LR method. The significant
PS model suggested by LR method comes out to be the same as the best performing
PS model in ANN approach for each stock (PSM5) determining R14, K14 and
D3 as significant independent variables. Comparison of the correlations
of outputs of ANN and LR methods with actual values for the same PS model
and for each stock are given in Table 4. Two-tailed
t-test applied to correlations show that in the 95% confidence interval,
ANN approach method has scored significantly (p = 0.000020) higher than
the LR method in terms of successful outcomes.
| Table 2: | Success rates of the application of ANNM3.11.1 to PSM5 |
| Table 3: | Correlations between the predicted outputs of ANNM3.11.1-PSM5 models and the actual price direction data for the results of both software |
| Table 4: | Correlations of outputs of ANN and LR methods with actual values for PSM5 |
CONCLUSION
This study is aimed at finding the best PS and ANN models for the prediction of the stock price direction using five chosen financial indicators and at showing that ANN model outperforms LR model in prediction. For this purpose; a software library package is developed; a total of 810 sets of predictions, which result from the application of 30 combinations of PS and ANN models to 27 stocks, are produced; developed software package is tested against a commercial ANN software and LR method is applied using the chosen financial indicators as independent variables.
Based on the results of this study it can be concluded that:
| • | The best PS model comes out to be PSM5 that has R14, K14 and D3 as financial indicators |
| • | The best ANN topology comes out to be ANNM3.11.1 that has three inputs, 11 hidden neurons in single hidden layer and one output |
| • | The developed software package performs statistically same as the commercial software |
| • | Results of LR method also determine PSM5 as the best PS model. |
| • | Comparison of ANN and LR methodologies has shown that ANN methodology statistically outperforms LR methodology |
| • | The results of the study have shown that there is sufficient empirical evidence that ISE-30 is not weak form efficient |
ACKNOWLEDGMENTS
Authors would like to thank Dr. Ali Tükel for his valuable suggestions and recommendations.