摘要
量化交易是近幾年來被熱烈討論的議題，它是藉由歷史數據經數學模型的分析預測，帶來更高獲利的策略，並且已有多篇文獻探討利用機器學習的方法來預測期貨價格。例如: 支持向量機器、隨機森林、遞迴式神經網路等。整體學習(ensemble learning)是一個結合機器學習預測以達到優化結果的方法，透過使多個模型互相學習，來降低預測的誤差來得到更加精確的結果。在這篇論文中，我們運用整體學習，整合上面提到的三個方法，並且比較使用整體學習的改善前後結果。我們通常透過預測未來的收盤價，來預測股市走勢及價格。過去文獻中使用的數據，是由每日的交易資料中，只取了一筆收盤價。在這次研究中，我們將會提升交易紀錄的頻率，一日使用將近四十筆的交易紀錄，並使用這個比過去大三十倍的資料量，來詳細並精準預測未來期貨的價格。我們使用的資料為2014年香港期貨交易所初始的真實交易數據，我們將資料轉換成欲使用的高頻率交易資料，並透過整體學習的方法，預測過去中的未來價格，由真實資料反映出這篇研究結果的準確性。

The method of predicting futures price is popularly discussed in recent year. The algorithms of machine learning are used in past several researches and successfully predicting the trend of futures market. In this research, we use ensemble learning to predict the price of stock index futures. The feature is the historical trading data that is the raw data from Hong Kong futures Exchange. We transform the raw data to high frequency sequential data, then we apply ensemble learning to combine the result, bagging, boosting and random subspace are the three main ensemble methods adopt in this paper. We select support vector regression, random forest and recurrent neural network to construct the libraries of models, and then we improve the result of the libraries of models by ensembling the results. Observing the numerical result, the performance of ensemble learning is compared with the result of single model, and the predicting error of ensemble learning is lower than SVR, RNN and RF.

Breiman, L. (1996). Bagging predictors. Machine learning, 24(2), 123-140.
Breiman, L. (2001). Random forests. Machine learning, 45(1), 5-32.
Cao, L. J., & Tay, F. E. H. (2003). Support vector machine with adaptive parameters in financial time series forecasting. IEEE Transactions on neural networks, 14(6), 1506-1518.
Caruana, R., Niculescu-Mizil, A., Crew, G., & Ksikes, A. (2004). Ensemble selection from libraries of models. In Proceedings of the twenty-first international conference on Machine learning (p. 18). ACM.
Cherkauer, K. J. (1996). Human expert-level performance on a scientific image analysis task by a system using combined artificial neural networks. In Working notes of the AAAI workshop on integrating multiple learned models, 21.
Coulibaly, P., & Baldwin, C. K. (2005). Nonstationary hydrological time series forecasting using nonlinear dynamic methods. Journal of Hydrology, 307(1-4), 164-174.
Deng, Y. F., Jin, X., & Zhong, Y. X. (2005). Ensemble SVR for prediction of time series. In Machine Learning and Cybernetics,. Proceedings of 2005 International Conference on, 6(3528-3534). IEEE.
Das, S. P., & Padhy, S. (2012). Support vector machines for prediction of futures prices in Indian stock market. International Journal of Computer Applications, 41(3).
Funahashi, K. I., & Nakamura, Y. (1993). Approximation of dynamical systems by continuous time recurrent neural networks. Neural networks, 6(6), 801-806.
Freund, Y. (1995). Boosting a weak learning algorithm by majority. Information and computation, 121(2), 256-285.
Freund, Y., & Schapire, R. E. (1996). Experiments with a new boosting algorithm. In Icml, 96(148-156).
Freund, Y., & Schapire, R. E. (1997). A decision-theoretic generalization of on-line learning and an application to boosting. Journal of computer and system sciences, 55(1), 119-139.
Guo, Z., Wang, H., Liu, Q., & Yang, J. (2014). A feature fusion based forecasting model for financial time series. PloS one, 9(6).
Grigoryan, H. (2016). A Stock Market Prediction Method Based on Support Vector Machines (SVM) and Independent Component Analysis (ICA). Database Systems Journal, 7(1), 12-21.
Ho, T. (1998). The random space method for constructing decision forests. IEEE Transactions on Pattern Analysis and Machine Intelligence, 20(8), 832–844.
Hüsken, M., & Stagge, P. (2003). Recurrent neural networks for time series classification. Neurocomputing, 50, 223-235.
Kaastra, I., & Boyd, M. (1996). Designing a neural network for forecasting financial and economic time series. Neurocomputing, 10(3), 215-236.
Kaneko, H., & Funatsu, K. (2014). Adaptive soft sensor based on online support vector regression and Bayesian ensemble learning for various states in chemical plants. Chemometrics and Intelligent Laboratory Systems, 137, 57-66.
Kane, M. J., Price, N., Scotch, M., & Rabinowitz, P. (2014). Comparison of ARIMA and Random Forest time series models for prediction of avian influenza H5N1 outbreaks. BMC bioinformatics, 15(1), 276.
Khaidem, L., Saha, S., & Dey, S. R. (2016). Predicting the direction of stock market prices using random forest. arXiv preprint arXiv:1605.00003.
Kotsiantis, S., & Kanellopoulos, D. (2012). Combining bagging, boosting and random subspace ensembles for regression problems. International Journal of Innovative Computing, Information and Control, 8(6), 3953-3961.
Linghu, B., & Sun, B. (2010, October). Constructing effective SVM ensembles for image classification. In Knowledge Acquisition and Modeling (KAM), 2010 3rd International Symposium on (80-83). IEEE.
Montague, D(2016). Algorithmic Trading of Futures via Machine Learning.
Mei, J., He, D., Harley, R., Habetler, T., & Qu, G. (2014). A random forest method for real-time price forecasting in new york electricity market. In PES General Meeting| Conference & Exposition, (1-5). IEEE.
Müller, K. R., Smola, A., Rätsch, G., Schölkopf, B., Kohlmorgen, J., & Vapnik, V. (1999). Using support vector machines for time series prediction. Advances in kernel methods—support vector learning, 243-254.
Narayanan, B., & Govindarajan, M. (2015). Prediction of Stock Market using Ensemble Model. International Journal of Computer Applications, 128(1), 18-21.
Pascanu, R., Gulcehre, C., Cho, K., & Bengio, Y. (2013). How to construct deep recurrent neural networks. arXiv preprint arXiv:1312.6026.
Raftery, A. E., Madigan, D., & Hoeting, J. A. (1997). Bayesian model averaging for linear regression models. Journal of the American Statistical Association, 92(437), 179-191.
Schapire, R. E. (1990). The strength of weak learnability. Machine learning, 5(2), 197-227.
Selvin, S., Vinayakumar, R., Gopalakrishnan, E. A., Menon, V. K., & Soman, K. P. (2017). Stock price prediction using LSTM, RNN and CNN-sliding window model. In Advances in Computing, Communications and Informatics (ICACCI), International Conference on (1643-1647). IEEE.
Segal, M. R. (2004). Machine learning benchmarks and random forest regression.
Specht, D. F. (1991). A general regression neural network. IEEE transactions on neural networks, 2(6), 568-576.
Smola, A. J., & Schölkopf, B. (2004). A tutorial on support vector regression. Statistics and computing, 14(3), 199-222.
Thissen, U., Van Brakel, R., De Weijer, A. P., Melssen, W. J., & Buydens, L. M. C. (2003). Using support vector machines for time series prediction. Chemometrics and intelligent laboratory systems, 69(1-2), 35-49.
Wang, S., Yu, L., Tang, L., & Wang, S. (2011). A novel seasonal decomposition based least squares support vector regression ensemble learning approach for hydropower consumption forecasting in China. Energy, 36(11), 6542-6554.
Wang, D., Yue, C., Wei, S., & Lv, J. (2017). Performance analysis of four decomposition-ensemble models for one-day-ahead agricultural commodity futures price forecasting. Algorithms, 10(3), 108.
Yang, J., Rao, R., Hong, P., & Ding, P. (2016). Ensemble model for stock price movement trend prediction on different investing periods. In Computational Intelligence and Security (CIS), 12th International Conference on (358-361). IEEE.
Zhang, J. S., & Xiao, X. C. (2000). Predicting chaotic time series using recurrent neural network. Chinese Physics Letters, 17(2), 88.
Zambelli, M., & Demiris, Y. (2017). Online multimodal ensemble learning using self-learned sensorimotor representations. IEEE Transactions on Cognitive and Developmental Systems, 9(2), 113-126.