本研究嘗試整合類神經網路與法則基礎（rule-based）系統技術，以建立S&P 500指數期貨的交易策略。本研究不同於先前研究之處有下列二方面：一、本研究採用法則基礎系統的方式提供神經網路的訓練範例；二、本研究以理解神經網路（Reasoning Neural Networks）取代後向傳導網路（Back propagation networks）以解決局部最小值與隱藏結點數未知的困境，而實證結果也顯示理解神經網路之表現優於後向傳導網路。首先，由期貨的日價格資料計算出十種技術分析指標值，用這些指標值來表示期貨市場內的各種可能狀況（case）。接著，我們提出FFM（Futures Forecast Model）與EFFM（Extended Futures Forecast Model）來處理市場的各種狀況，預測出隔日的期貨價格改變方向。以法則基礎方法所建立的FFM是用來處理明顯的狀況（obvious cases），並且提供類神經網路好的訓練範例。而EFFM包括四個理解神經網路系統與一個決策機置（voting mechanism），它被用來處理那些不明顯的狀況（non-obvious

cases）。從實證模擬的結果顯示，在預測市場時FFM與EFFM有良好的合作

關係。因此，我們以FFM與EFFM為基礎建立一個整合的期貨交易系統（Integrated Futures Trading System，IFTS），並將它用於S&P 500 指數期貨市場作模擬交易，結果我們發現在1988到1993年的測試期間，IFTS

的投資報酬率高於買入持有投資策略。

This research adopts a hybrid approach to implementing the

trading strategies in the S&P 500 index futures market. The

hybrid approach integrates both the rule-based systems technique and the neural networks technique. Our methodology is different from previous studies in two aspects. First, we employ Reasoning Neural Networks (RN) instead of back propagation networks to resolve the undesired predicaments of local minimum and the unknown of the number of hidden nodes. Second, the rule-based systems approach is applied to provide neural networks with good

training examples. We, first, categorize the daily conditions of the futures market into a variety of cases through processing futures historical data. Then, the dual-forecast models, FFM (futures forecast model) and EFFM (extended futures forecast model), are proposed to predict the direction of daily price changes. The rule-based model, FFM, is designed to deal with the obvious cases and to provide the neural network-based model, EFFM, with good training examples. Meanwhile, EFFM, which consists of four RNs and a voting mechanism, is designed to handle the non-obvious cases. The simulation results show that the cooperation of FFM and EFFM does a good job in predicting

the direction of daily price change of S&P 500 index futures.

Based on FFM and EFFM, the integrated futures trading system

(IFTS) is developed and employed to trade the S&P 500 index

futures contracts. The results show that IFTS outperforms the passive buy-and-hold investment strategy over the six-year testing period from 1988 to 1993.

Bergerson, Karl and Donald C. Wunsch (1991), "A Commodity Trading Model Based on a Neural Network - Expert System Hybrid," Proceedings of the IEEE International Conference on Neural Networks, pp. 1289-1293.
Blank, S. C. (1991), "Chaos' in Futures Market? A Nonlinear Dynamical Analysis," Journal of Futures Markets, Vol. 11:711-728.
Bosarge, W. E. (1991), "Adaptive Processes to Exploit the Nonlinear Structure of Financial Markets," The Santa Fe Institute of Complexity Conference: Neural Networks and Pattern Recognition in Forecasting Financial Markets, February 15.
Bryson, AE. and y-c. Ho (1969), Applied Optimal Control, New York: Blaisdell.
Chande, Tushar S. and Stanley Kroll (1994), The New Technical Trader, New York: John Wiley and Sons, Inc.
DeCoster, G, P., Labys, W.C., and Mitchell, D. W. (1992), ''Evidence of Chaos in Commodity Futures Prices," Journal of Futures A1al'kets, Vol. 12:291-305.
Frank, M, and Stengos, T. (1989), "Measuring the Strangeness of Gold and Silver Rates of Return," Review of Economic Studies, Vol. 56:553-567.
Freeman, James A and David M, Skapura (1992), Neural Networks Algorithms. Applications, and Programming Techniques, Addison-Wesley, Reading MA
Grudnitski, Gary and Larry Osburn (1993), "Forecasting S&P and Gold Futures Prices:An Application of Neural Networks," Journal of Futures Markets, Vol. 13, No. 6,631-643 .
Herbst, Anthony F. (1992), Analyzing and Forecasting Futures Prices, New York: John Wiley and Sons, Inc.
Herbst, Anthony F. and C. W. Slinkman (1984), "Does the Evidence Support the Existence of 'Political Economic' Cycles in the U.S. Stock Market?", Financial Analyst Journal, Vol. 40, No.2, March.
Hutchinson, James M., Andrew W. Lo, and Tomaso Poggio (1994), "A N onparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks,"Journal of Finance, Vol. 49, No.3, 851-889.
Kee, Wong Yue and Annie Koh (1994), "Technical Analysis of Nikkei 225 Stock Index Futures Using an Expert System Advisor," Proceedings of the CBOT Conference.Minsky, M.L. and S.A. Papert (1969), Perceptrons, Cambridge: MIT Press.
Parker, D.D. (1985), "Learning Logic," Technical Report TR-47, Center for Computational Research in Economics and Management Science, Massachusetts Institute of Technology, Cambridge, MA.
Rosenblatt, F. (1958), "The Perceptron: A Probabilistic Model for Information Storage and Organization in the Brain." Psychological Review, Vol. 65, pp.3 86-408.
Rosenblatt, F. (1962), Principles ofneurodynamics, New York: Spartan Books.
Rumelhart, D. E., Hinton, G. E., and Williams, R. J. (1986), "Learning internal representations by error propagation," Parallel Distributed Processing, Vol. 1, pp.318-62, Cambrideg, MA: MIT Press.
Smith, Murray (1993), Neural Networks for Statistical Modeling, New York: Van Nostrand Reinhold.
Trippi, Robert R. and Duane DeSieno (1992), "Trading Equity Index Futures wjth a Neural Network," Journal of Portfolio Management, Fall 1992, pp. 27-33.
Trippi, Robert R., and Turban, E. (1993), Neural Networks ill Finance and Investing, Chicago: Probus Publishing.
Turban, E. (1990), Decision Support and Expert Systems, New York: Macmillan Publishing Company.
Tsaih, R. (1993), "The Softening Learning Procedure," Mathematical and Computer Modebng, Vol. 18, No.8, pp. 61-64.
Tsaih, R. (1995), "The Reasoning Neural Networks," Annals of Mathematics and Artificial Intelligence, forthcoming.
Tsaih, R. (1996), ''Learning Procedure that Guarantees Obtaining the Desired Solution Of the 2-Classes Categorization Learning Problem," class-note.
Werbos, P.J. (1974), "Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences," Ph.D. Thesis, Harvard University, Cambridge, MA.