استفاده از داده کاوی و شبکه های عصبی برای پیش بینی بازدهی بازار سهام

It has been widely accepted by many studies that non-linearity exists in the financial markets and that neural networks can be effectively used to uncover this relationship. Unfortunately, many of these studies fail to consider alternative forecasting techniques, the relevance of input variables, or the performance of the models when using different trading strategies. This paper introduces an information gain technique used in machine learning for data mining to evaluate the predictive relationships of numerous financial and economic variables. Neural network models for level estimation and classification are then examined for their ability to provide an effective forecast of future values. A cross-validation technique is also employed to improve the generalization ability of several models. The results show that the trading strategies guided by the classification models generate higher risk-adjusted profits than the buy-and-hold strategy, as well as those guided by the level-estimation based forecasts of the neural network and linear regression models.

Over the past two decades many important changes have taken place in the environment of financial markets. The development of powerful communication and trading facilities has enlarged the scope of selection for investors (Elton and Gruber, 1991). Traditional capital market theory has also changed and methods of financial analysis have improved (Poddig and Rehkugler, 1996). Forecasting stock return or a stock index is an important financial subject that has attracted researchers' attention for many years. It involves an assumption that fundamental information publicly available in the past has some predictive relationships to the future stock returns or indices. The samples of such information include economic variables such as interest rates and exchange rates, industry specific information such as growth rates of industrial production and consumer price, and company specific information such as income statements and dividend yields. This is opposed to the general perception of market efficiency (Fama, 1970). In fact, the efficient market hypothesis states that all available information affecting the current stock values is constituted by the market before the general public can make trades based on it (Jensen, 1978). Therefore, it is impossible to forecast future returns since they already reflect all information currently known about the stocks. This is still an empirical issue because there is considerable evidence that markets are not fully efficient, and it is possible to predict the future stock returns or indices with results that are better than random (Lo and MacKinlay, 1988). Recently, Balvers, Cosimano, and McDonald (1990), Breen, Glosten, and Jagannathan (1990), Campbell (1987), Fama and Schwert (1977), Fama and French, 1988 and Fama and French, 1989, Ferson (1989), Keim and Stambaugh (1986), and Schwert (1990) among others, provide evidence that stock market returns are predictable by means of publicly available information such as time-series data on financial and economic variables, especially those with an important business cycle component. These studies identify that such variables as various interest rates, monetary growth rates, changes in industrial production, and inflation rates are statistically important for predicting a portion of the stock returns. However, most of the above studies attempting to capture the relationship between the available information and the stock returns rely on simple linear regression assumptions. There is no evidence to support the assumption that the relationship between the stock returns and the financial and economic variables is perfectly linear. This is due to the fact that there exists the significant residual variance of the actual stock return from the prediction of the regression equation. Therefore, it is possible that nonlinear models are able to explain this residual variance and produce more reliable predictions of the stock price movements (Mills, 1990; Priestley, 1988). Since many of the current modeling techniques are based on linear assumptions, a new kind of financial analysis that considers the nonlinear analysis of integrated financial markets needs to be considered. Even though there exists a number of non-linear regression techniques, most of these techniques require that the non-linear model must be specified before the estimation of parameters can be determined. One non-linear modeling technique that may overcome these problems involves the use of neural networks (Hill, O'Connor, and Remus, 1996). In fact, neural networks offer a novel technique that does not require a pre-specification during the modeling process because they independently learn the relationship inherent in the variables. This is especially useful in security investment and other financial areas where much is assumed, and little is known about the nature of the processes determining asset prices (Burrell and Folarin, 1997). Neural networks also offer the flexibility of numerous architecture types, learning algorithms, and validation procedures. As a result, the discovery and use of non-linearity in financial market movements and analysis to produce better predictions of future stock returns or indices has been greatly emphasized by various researchers and financial analysts during the last few years (see Abhyankar, Copeland, and Wong, 1997). Current studies that reflect an interest in applying neural networks to answer future stock behaviors include Chenoweth and Obradovic (1996), Desai and Bharati (1998), Gencay (1998), Leung, Daouk, and Chen (2000), Motiwalla and Wahab (2000), Pantazopoulos et al. (1998), Qi and Maddala (1999), and Wood and Dasgupta (1996). To this end, it has been found that stock trading driven by a certain forecast with a small forecasting error may not be as profitable as trading guided by an accurate prediction of the sign of stock return (Aggarwal and Demaskey, 1997; Leung et al., 2000; Maberly, 1986; Wu and Zhang, 1997). Nonetheless, having an accurate prediction of a certain stock or stock index return still has numerous benefits. Given the existence of a vast number of articles addressing the predictabilities of stock market return, most of the proposed models relied on various assumptions and often employ a particular series of input variables without justification as to why they were chosen. Obviously, a systematic approach to determine what inputs are important is necessary. In regard to this, the present paper will begin with the discussion of the methodology for data selection and then introduce an information gain data mining technique for performing the variable relevance analysis. Two neural network approaches that can be used for classification and level estimation will also be briefly reviewed in the third section, followed by a discussion of the neural network models, including the generalized regression, probabilistic, and multi-layer feed-forward neural networks that were developed to estimate the value (level) and classify the direction (sign) of excess stock returns on the S&P 500 stock index portfolio. In addition, the five-fold cross validation and early stopping techniques were also implemented in this study to improve the generalization ability of the feed-forward neural networks. The resulting data selection and model development, empirical results, and discussion and conclusion will then be presented, respectively. Finally, the data sources and descriptions are given in the Appendix.

An attempt has been made in this study to investigate the predictive power of financial and economic variables by adopting the variable relevance analysis technique in machine learning for data mining. This approach seems particularly attractive in selecting the variables when the usefulness of the data is unknown, especially when non-linearity exists in the financial market as found in this study. Since it has been long known that the determinant between the variables and their interrelationships over stock returns could change over time, different relevant input variables may be obtained by conducting this data mining technique under different time periods. In particular, we examined the effectiveness of the neural network models used for level estimation and classification. The results show that the trading strategies guided by the neural network classification models generate higher profits under the same risk exposure than those suggested by the other strategies, including the buy-and-hold strategy, as well as the level estimation forecasts of neural network and linear regression models. More importantly, it is found that the highest profitability improvement guided by the Portfolio Class NN model is consistent with its three superior performance measures, namely the Pearson correlation, the root-mean squared error, and the correct sign of excess stock return. However, it can be observed from several forecasting models that better results of performance measurement do not always imply higher profitability. For instance, the GRNN model has better results of all three performance measures than the Original Level NN model does, yet it does not outperform the Original Level NN model in terms of the profits obtained from trading. This suggests that the forecast that has a higher percentage of correct sign may not necessarily yield higher profit. In fact, it may be due to the fact that the Original Level NN model gives better prediction of signs when the actual monthly stock return is highly volatile, thus receiving higher trading profits. This observation suggests the importance of making an accurate asset allocation (between stock and T-bill) when the positive or negative actual stock return of the next month is significant. Therefore, potentially higher investment return may be obtained from training the networks to correctly predict the signs of trading only when significant profit opportunities exist. The above empirical results show that the trading results based on several neural network forecasts can arrive at higher profitability improvement than the buy-and-hold strategies. However, this does not mean that the efficient market hypothesis can be totally ignored. The reason being that the buy-and-hold account can also be very profitable. In fact, the profitability obtained from the neural network forecasts will likely be less if transaction costs are taken into consideration. Feed-forward neural network training is usually not very stable since the training process may depend on the choice of a random start. Training is also computationally expensive in terms of the training times used to determine the appropriate network structure. The degree of success, therefore, may fluctuate from one training pass to another. Although the portfolio neural networks yield impressive profits on average, it should raise concern that higher profits are derived at the expense of exposing the investors to higher risk. Nonetheless, the empirical findings in this study show that our proposed development of the portfolio network models using the n-fold cross-validation and early stopping techniques does not sacrifice any of the first period data used for training and validating the networks. This is especially useful when the data size is limited. In particular, we find that the method for improving the generalization ability of feed-forward neural networks, a combination of n-fold cross-validation and early stopping techniques, clearly help improve the out-of-sample forecasts. In addition to the early stopping advantage, improvement may be due to the fact that five-time network modeling allows the networks to extract more useful information from the data. Thus, the prediction based on the weighted excess return or the majority of excess return sign could effectively be used to reduce the prediction error. As a result, the portfolio network models for both classification and level estimation consistently outperform the linear regression, the generalized regression neural network, the probabilistic neural network, and the buy-and-hold account. More interestingly, the Sign Port Level NN model is able to generate a higher return than the models employing the level of excess stock returns. This strongly suggests that the portfolio neural networks that direct the trading based on the majority of the five network outputs can be developed and used as a more efficient forecasting tool. In conclusion, both researchers and practitioners have studied stock market prediction for many years. Many studies conclude that stock returns can be predicted by some financial and economic variables. To this end, our finding suggests that financial forecasting is always and will remain difficult since such data are greatly influenced by economical, political, international, and even natural events. Obviously, this study covers only fundamental available information, while the technical analysis approach remains intact. It is far from perfect as the technical analysis has been proved to provide invaluable information during stock price and stock return forecasting and to some extent has been known to offer a relative mixture of human, political, and economical events. In fact, there are many studies done by both academics and practitioners in this area. If both technical and fundamental approaches are thoroughly examined and included during the variable relevance analysis modeling, it would no doubt be a major improvement in predicting stock returns. This study assumes trading strategies of investing in either the stock index portfolio or risk-free account in the absence of trading costs. During the simulated trading exercise, the authors also noticed that the profitability results could change if a different trading strategy was adopted by investors. In fact, it is possible that investors would benefit from further investigation on profits received from different trading decisions. Finally, future research should consider the trading simulation under the scenarios of stock dividends, transaction costs, and individual-tax brackets to replicate the realistic investment practices.