Stock price prediction has attracted much attention from both practitioners and researchers. However, most studies in this area ignored the non-stationary nature of stock price series. That is, stock price series do not exhibit identical statistical properties at each point of time. As a result, the relationships between stock price series and their predictors are quite dynamic. It is challenging for any single artificial technique to effectively address this problematic characteristics in stock price series. One potential solution is to hybridize different artificial techniques. Towards this end, this study employs a two-stage architecture for better stock price prediction. Specifically, the self-organizing map (SOM) is first used to decompose the whole input space into regions where data points with similar statistical distributions are grouped together, so as to contain and capture the non-stationary property of financial series. After decomposing heterogeneous data points into several homogenous regions, support vector regression (SVR) is applied to forecast financial indices. The proposed technique is empirically tested using stock price series from seven major financial markets. The results show that the performance of stock price prediction can be significantly enhanced by using the two-stage architecture in comparison with a single SVR model.
Stock price prediction is an important financial subject that has attracted researchers’ attention for many years. In the past, conventional statistical methods were employed to forecast stock price. However, stock price series are generally quite noisy and complex. To address this, numerous artificial techniques, such as artificial neural networks (ANN) or genetic algorithms are proposed to improve the prediction results (see Table 1). Recently, researchers are using support vector regressions (SVRs) in this area (see Table 1). SVR was developed by Vapnik and his colleagues (Vapnik, 1995). Most comparison results show that prediction performance of SVR is better than that of ANN (Huang et al., 2005, Kim, 2003 and Tay and Cao, 2001a). Reasons that are often cited to explain this superiority include the face that SVRs implement the structural risk minimization principle, while ANNs use the empirical risk minimization principle. The former seeks to minimize the misclassification error or deviation from correct solution of the training data; whereas the latter seeks to minimize the upper bound of generalization error. Solution of SVR may be global optimum while neural network techniques may offer only local optimal solutions. Besides, in choosing parameters, SVRs are less complex than ANNs.
Although researchers have shown that SVRs can be a very useful for stock price forecasting, most studies ignore that stock price series are non-stationary. That is, stock price series do not exhibit identical statistical properties at each point of time and face dynamic changes in the relationship between independent and dependent variables. Such structural changes, which are often caused by political events, economic conditions, traders’ expectations and other environmental factors, are an important characteristic of equities’ price series. This variability makes it difficult for any single artificial technique to capture the non-stationary property of the data. Most artificial algorithms require a constant relationship between independent and dependent variables, i.e., the data presented to artificial algorithms is generated according to a constant function. One potential solution is to hybridize several artificial techniques. For example, Tay and Cao (2001b) suggest a two-stage architecture by integrating a self-organizing map (SOM) and SVR to better capture the dynamic input–output relationships inherent in the financial data. This architecture was originally proposed by Jacobs, Jordan, Nowlan, and Hinton (1991), who were inspired by the divide-and-conquer principle that is often used to attack complex problems, i.e., dividing a complex problem into several smaller and simpler problems so that the original problem can be easily solved. In the two-stage architecture, the SOM serves as the “divide” function to decompose the whole financial data into regions where data points with similar statistical distribution are grouped together. After decomposing heterogeneous data into different homogenous regions, SVRs can better forecast the financial indices. Although this architecture is interesting and promising, Tay and Cao (2001b) tested the effectiveness of the architecture only on futures and bonds. Whether the architecture can be employed for stock price prediction remains to be answered.
This study aims to test the effectiveness of the architecture for stock price prediction by comparing the predictive performance of the two-stage architecture with a single SVM technique. Seven stock market indices were used for this study. This paper consists of five sections. Section 2 introduces the basic concept of SVR, SOM and the two-stage architecture. Section 3 describes research design and experiments. Section 4 presents the conclusions.
The study shows that the performance of stock price prediction can be significantly enhanced by using the two-stage architecture in comparison with a single SVM model. The results may be attributable to the fact that financial time series are non-stationary and, therefore, the two-stage architecture can better capture the characteristics by decomposing the whole financial series into smaller homogenous regions. After decomposing the data, SVRs can better predict financial indices. The results suggest that the two-stage architecture provides a promising alternative for financial time series forecasting. Future research can further testing the idea of the two-stage architecture on other non-stationary data to evaluate the generalizability of the architecture.
