Elsevier

Neurocomputing

Volume 70, Issues 4–6, January 2007, Pages 697-703
Neurocomputing

Flexible neural trees ensemble for stock index modeling

https://doi.org/10.1016/j.neucom.2006.10.005Get rights and content

Abstract

The use of intelligent systems for stock market predictions has been widely established. In this paper, we investigate how the seemingly chaotic behavior of stock markets could be well represented using flexible neural tree (FNT) ensemble technique. We considered the Nasdaq-100 index of Nasdaq Stock MarketSM and the S&P CNX NIFTY stock index. We analyzed 7-year Nasdaq-100 main index values and 4-year NIFTY index values. This paper investigates the development of novel reliable and efficient techniques to model the seemingly chaotic behavior of stock markets. The structure and parameters of FNT are optimized using genetic programming (GP) like tree structure-based evolutionary algorithm and particle swarm optimization (PSO) algorithms, respectively. A good ensemble model is formulated by the local weighted polynomial regression (LWPR). This paper investigates whether the proposed method can provide the required level of performance, which is sufficiently good and robust so as to provide a reliable forecast model for stock market indices. Experimental results show that the model considered could represent the stock indices behavior very accurately.

Introduction

Prediction of stocks is generally believed to be a very difficult task—it behaves like a random walk process and time varying. The obvious complexity of the problem paves the way for the importance of intelligent prediction paradigms. During the last decade, stocks and futures traders have come to rely upon various types of intelligent systems to make trading decisions [1], [2], [3], [4], [10], [15], [22], [14]. Several intelligent systems have in recent years been developed for modeling expertise, decision support and complicated automation tasks [15], [17], [23], [28], [18].

Leigh et al. [16] introduced a method for combining template matching, using pattern recognition and a feed-forward neural network, to forecast stock market activity. The authors evaluated the effectiveness of the method for forecasting increases in the New York Stock Exchange Composite Index at a 5 trading day horizon. Results indicate that the technique is capable of returning results that are superior to those attained by random choice.

Kim and Chun [13] explored a new architecture for graded forecasting using an arrayed probabilistic network (APN) and used a “mistake chart” to compare the accuracy of learning systems against default performance based on a constant prediction. Authors also evaluated several backpropagation models against a recurrent neural network (RNN) as well as probabilistic neural networks, etc.

Tsaih et al. [26] investigated a hybrid AI (artificial intelligence) approach to the implementation of trading strategies in the S&P 500 stock index futures market. The hybrid AI approach integrates the rule-based systems technique and the neural networks technique to accurately predict the direction of daily price changes in S&P 500 stock index futures. By highlighting the advantages and overcoming the limitations of both the neural networks technique and rule-based systems technique, the hybrid approach can facilitate the development of more reliable intelligent systems to model expert thinking and to support the decision-making processes.

Refenes et al. [24] proposed a simple modification to the error backpropagation procedure which takes into account gradually changing input–output relations. The procedure is based on the principle of discounted least squares whereby learning is biased towards more recent observations with long term effects experiencing exponential decay through time. This is particularly important in systems in which the structural relationship between input and response vectors changes gradually over time but certain elements of long term memory are still retained. The procedure is implemented by a simple modification of the least-squares cost function commonly used in error backpropagation.

Van den Berg et al. [27] proposed a probabilistic fuzzy systems to develop financial models where one can identify different states of the market for modifying ones actions. Authors developed a Takagi-Sugeno (TS) probabilistic fuzzy systems that combine interpretability of fuzzy systems with the statistical properties of probabilistic systems. The methodology is applied to financial time series analysis and demonstrated how a probabilistic TS fuzzy system can be identified, assuming that a linguistic term set is given.

From the perspective of the agent-based model of stock markets, Chen and Liao [5] examined the possible explanations for the presence of the causal relation between stock returns and trading volume. Using the agent-based approach, the authors found that the explanation for the presence of the stock price volume relation may be more fundamental. Conventional devices such as information asymmetry, reaction asymmetry, noise traders or tax motives are not explicitly required. Authors claimed that a full understanding of the price volume relation cannot be accomplished unless the feedback relation between individual behavior at the bottom and aggregate phenomena at the top is well understood.

In this paper, we analyzed the seemingly chaotic behavior of two well-known stock indices namely the Nasdaq-100 index of NasdaqSM [20] and the S&P CNX NIFTY stock index [21]. The Nasdaq-100 index reflects Nasdaq's largest companies across major industry groups, including computer hardware and software, telecommunications, retail/wholesale trade and biotechnology [20]. The Nasdaq-100 index is a modified capitalization-weighted index, which is designed to limit domination of the Index by a few large stocks while generally retaining the capitalization ranking of companies. Through an investment in the Nasdaq-100 index tracking stock, investors can participate in the collective performance of many of the Nasdaq stocks that are often in the news or have become household names. Similarly, S&P CNX NIFTY is a well-diversified 50 stock index accounting for 25 sectors of the economy [21]. It is used for a variety of purposes such as benchmarking fund portfolios, index-based derivatives and index funds. The CNX Indices are computed using market capitalization weighted method, wherein the level of the Index reflects the total market value of all the stocks in the index relative to a particular base period. The method also takes into account constituent changes in the index and importantly corporate actions such as stock splits, rights, etc. without affecting the index value.

Our research is to investigate the performance analysis of FNT [7], [9], [6] ensemble for modeling the Nasdaq-100 and the NIFTY stock market indices. The hierarchical structure of FNT is evolved using GP with specific instructions. The parameters of the FNT model are optimized by PSO algorithm [12]. The proposed method interleaves both optimizations. Starting with random structures and corresponding parameters, it first tries to improve the structure and then as soon as an improved structure is found, it fine tunes its parameters. It then goes back to improving the structure again and, fine tunes the structure and rules’ parameters. This loop continues until a satisfactory solution is found or a time limit is reached. The novelty of this paper is in the usage of flexible neural trees ensemble for selecting the important inputs and/or time delays and for forecasting models.

We analyzed the Nasdaq-100 index value from 11 January 1995 to 11 January 2002 [20] and the NIFTY index from 01 January 1998 to 03 December 2001 [21]. For both the indices, we divided the entire data into almost two equal parts. No special rules were used to select the training set other than ensuring a reasonable representation of the parameter space of the problem domain [3].

The rest of the paper is organized as follows. The flexible neural tree model and its design method are given in Section 2. Some simple and FNT ensemble approaches are presented in Section 3. Some simulation results on stock index modeling are shown in Section 4. Finally in Section 5, we present some conclusions and future works.

Section snippets

The flexible neural tree model

The function set F and terminal instruction set T used for generating a FNT model are described as S=FT={+2,+3,,+N}{x1,,xn}, where +i(i=2,3,,N) denote non-leaf nodes’ instructions and taking i arguments. x1,x2,,xn are leaf nodes’ instructions and taking no other arguments. The output of a non-leaf node is calculated as a flexible neuron model (see Fig. 1). From this point of view, the instruction +i is also called a flexible neuron operator with i inputs.

In the creation process of neural

The FNT ensemble

For most regression and classification problems, combining the outputs of several predictors improves on the performance of a single generic one [25]. Formal support to this property is provided by the so-called bias/variance dilemma [11], based on a suitable decomposition of the prediction error. According to these ideas, good ensemble members must be both accurate and diverse, which poses the problem of generating a set of predictors with reasonably good individual performances and

Experiments

We considered 7-year stock data for the Nasdaq-100 Index and 4-year for the NIFTY index. Our target is to develop efficient forecast models that could predict the index value of the following trade day based on the opening, closing and maximum values of the same on a given day. The assessment of the prediction performance of the different ensemble paradigms were done by quantifying the prediction obtained on an independent data set. The root mean squared error (RMSE), maximum absolute

Conclusions

In this paper, we have demonstrated how the chaotic behavior of stock indices could be well represented by FNT ensemble learning paradigm. Empirical results on the two data sets using FNT ensemble models clearly reveal the efficiency of the proposed techniques. In terms of RMSE values, for the Nasdaq-100 index and the NIFTY index, LWPR performed marginally better than other models. For both indices (test data), LWPR also has the highest correlation coefficient and the lowest value of MAPE and

Acknowledgments

This research was partially supported by the Natural Science Foundation of China under grant number 60573065, and The Provincial Science and Technology Development Program of Shandong under Grant number SDSP2004-0720-03.

Yuehui Chen was born in 1964 in Shandong Province of China. He received his B.Sc. degree in mathematics/automatics from the Shandong University of China in 1985, and Master and Ph.D. degree in electrical engineering from the Kumamoto University of Japan in 1999 and 2001. During 2001C2003, he had worked as the Senior Researcher of the Memory-Tech Corporation at Tokyo. Since 2003 he has been a member at the Faculty of Electrical Engineering in Jinan University, where he is currently head of the

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    Yuehui Chen was born in 1964 in Shandong Province of China. He received his B.Sc. degree in mathematics/automatics from the Shandong University of China in 1985, and Master and Ph.D. degree in electrical engineering from the Kumamoto University of Japan in 1999 and 2001. During 2001C2003, he had worked as the Senior Researcher of the Memory-Tech Corporation at Tokyo. Since 2003 he has been a member at the Faculty of Electrical Engineering in Jinan University, where he is currently head of the Laboratory of Computational Intelligence. His research interests include Evolutionary Computation, Neural Networks, Fuzzy Logic Systems, Hybrid Computational Intelligence and their applications in time-series prediction, system identification, intelligent control, intrusion detection systems, web intelligence and bioinformatics. He is the author and co-author of more than 70 technique papers. Professor Yuehui Chen is a member of IEEE, the IEEE Systems, Man and Cybernetics Society and the Computational Intelligence Society, a member of Young Researchers Committee of the World Federation on Soft Computing, and a member of CCF Young Computer Science and Engineering Forum of China. More information at: http://cilab.ujn.edu.cn

    Bo Yang is a professor and vice-president of Jinan University, Jinan, China. He is the Director of the Provincial Key Laboratory of Information and Control Engineering, and also acts as the Associate Director of Shandong Computer Federation, and Member of the Technical Committee of Intelligent Control of Chinese Association of Automation. His main research interests include computer networks, artificial intelligence, machine learning, knowledge discovery, and data mining. He has published numerous papers and gotten some of important scientific awards in this area.

    Ajith Abraham currently works as a Professor under the South Korean Government's Institute of Information Technology Assessment (IITA) Professorship program at Chung-Ang University, Korea. He is also a visiting researcher of Rovira i Virgili University, Spain and an Adjunct Professor of Jinan University, China and Dalian Maritime University, China. His primary research interests are in computational intelligence with a focus on using evolutionary computation techniques for designing intelligent paradigms. Application areas include Web services, information security, Web intelligence, financial modeling, multi-criteria decision-making, data mining, etc. He has authored/co-authored over 200 research publications in peer reviewed reputed journals, book chapters and conference proceedings of which three have won “best paper” awards. He is serving the Editorial board of over a dozen International Journals and has also guest edited 15 special issues for reputed International Journals. Since 2001, he is actively involved in the Hybrid Intelligent Systems (HIS) and the Intelligent Systems Design and Applications (ISDA) series of annual International conferences. He received PhD degree from Monash University, Australia. More information at: http://www.softcomputing.net

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