自我建構式複數模糊ARIMA於指數波動預測之研究

本研究提出一個自我建構式複數模糊類神經系統（Self-organizing complex neuro-fuzzy system, SOCNFS），結合差分自回歸移動平均模型（Autoregressive integrated moving average, ARIMA），形成SOCNFS-ARIMA模型並應用於時間序列預測之研究。此智慧型系統之學習過程分成結構學習階段（Structure learning phase）與參數學習階段（Parameter learning phase）兩階段。結構學習階段使用SC-based FCM分群演算法，自動決定符合樣本資料分布特性的系統架構與大小；參數學習階段使用粒子群最佳化演算法（Particle swarm optimization, PSO）與遞迴式最小平方估計器（Recursive least squares estimator, RLSE），稱為PSO-RLSE複合式學習演算法，進行系統參數之快速學習。本研究使用複數模糊集合（Complex fuzzy sets, CFSs）與差分自回歸移動平均模型的概念，分別應用在模糊規則的前鑑部與後鑑部，以增加處理複雜系統問題之映射能力。本研究設計五個實驗來驗證系統效能：Mackey-Glass混沌時間序列與星星亮度時間序列是指標性的序列，運用本研究之結果和過去文獻比較，可以了解本研究模型之可信度；實驗三至實驗五取自真實世界資料，實驗三的標準普爾500指數日波動序列實驗驗證加入複數模糊集合與ARIMA模型的效能；實驗四與實驗五測試同步預測不同時間序列的效能，道瓊工業平均指數與那斯達克綜合指數年波動時間序列實驗亦驗證轉換波動之不同取樣區間對於預測性能的差異；而標準普爾500指數與上海證券交易所股票價格綜合指數年波動時間序列實驗則證實本研究模型擁有同時預測兩個不同經濟體系資料的能力。實驗結果顯示本研究模型在證券股價指數波動預測上有良好效能。

關鍵字

PSO-RLSE複合式學習演算法； SC-based FCM分群演算法；差分自回歸移動平均模型；複數模糊類神經系統；指數波動預測；時間序列

並列摘要

A self-organizing intelligent approach, using complex fuzzy sets (CFSs), neuro-fuzzy theory, and autoregressive integrated moving average (ARIMA) model, is proposed to the problem of stock index volatility forecasting. The proposed computing system is called the self-organizing complex neuro-fuzzy system ARIMA (denoted as SOCNFS-ARIMA). A SC-based FCM clustering method, consisting of the subtractive clustering (SC) and the fuzzy c-means (FCM), is used to automatically determine the initial knowledge base of SOCNFS-ARIMA. The proposed approach has excellent functional mapping ability for prediction. The PSO-RLSE hybrid learning algorithm is proposed for the purpose of fast learning, integrating the particle swarm optimization (PSO) and the recursive least squares estimator (RLSE). To test the proposed approach, five experiments are conducted, including the Mackey-Glass chaos time series, the star brightness time series, the S&P 500 index, the Dow Jones Industrial Average (DJIA) index and the NASDAQ composite index, and the Shanghai Stock Exchange (SSE) composite index. According to the experimental results, for the first two experiments, the proposed approach has outperformed the compared approaches in the literature. The experimental results have exposed the merits of CFSs in the proposed approach and have shown successfully the practice of dual volatility prediction with excellent performance for two time series of stock market.

並列關鍵字

PSO-RLSE hybrid learning method ； SC-based FCM clustering algorithm ； autoregressive integrated moving average ； complex neuro-fuzzy system (CNFS) ； time series forecasting

參考文獻

[1]　Abu-mostafa, Y. S. and Atiya, A. F., “Introduction to financial forecasting,” Applied Intelligence, vol. 6, pp. 205-213, 1996.

[3]　Bailie, R. T. and DeGennaro, R. P., “Stock returns and volatility,” Journal of Financial and Quantitative Analysis, vol. 25, pp. 203-214, 1990.

[4]　Bezdek, J. C., Ehrlich, R. and Full, W., “FCM: the fuzzy c-means clustering algorithm,” Computers and Geosciences, vol. 10, pp. 191-203, 1984.

[5]　Black, F. and Scholes, M., “The pricing of options and corporate liabilities,” The Journal of Political Economy, vol. 81, no. 3, pp. 637-654, 1973.

[8]　Buckley, J. J., “Fuzzy complex numbers,” Fuzzy Sets and Systems, vol. 33, pp. 333-345, 1989.

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自我建構式複數模糊ARIMA於指數波動預測之研究

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