Support vector regression with chaos-based firefly algorithm for stock market price forecasting

Due to the inherent non-linearity and non-stationary characteristics of financial stock market price time series, conventional modeling techniques such as the Box-Jenkins autoregressive integrated moving average (ARIMA) are not adequate for stock market price forecasting. In this paper, a forecasting model based on chaotic mapping, firefly algorithm, and support vector regression (SVR) is proposed to predict stock market price. The forecasting model has three stages. In the first stage, a delay coordinate embedding method is used to reconstruct unseen phase space dynamics. In the second stage, a chaotic firefly algorithm is employed to optimize SVR hyperparameters. Finally in the third stage, the optimized SVR is used to forecast stock market price. The significance of the proposed algorithm is 3-fold. First, it integrates both chaos theory and the firefly algorithm to optimize SVR hyperparameters, whereas previous studies employ a genetic algorithm (GA) to optimize these parameters. Second, it uses a delay coordinate embedding method to reconstruct phase space dynamics. Third, it has high prediction accuracy due to its implementation of structural risk minimization (SRM). To show the applicability and superiority of the proposed algorithm, we selected the three most challenging stock market time series data from NASDAQ historical quotes, namely Intel, National Bank shares and Microsoft daily closed (last) stock price, and applied the proposed algorithm to these data. Compared with genetic algorithm-based SVR (SVR-GA), chaotic genetic algorithm-based SVR (SVR-CGA), firefly-based SVR (SVR-FA), artificial neural networks (ANNs) and adaptive neuro-fuzzy inference systems (ANFIS), the proposed model performs best based on two error measures, namely mean squared error (MSE) and mean absolute percent error (MAPE).

[1]  James V. Hansen,et al.  Neural networks and traditional time series methods: a synergistic combination in state economic forecasts , 1997, IEEE Trans. Neural Networks.

[2]  Pei-Chann Chang,et al.  A TSK type fuzzy rule based system for stock price prediction , 2008, Expert Syst. Appl..

[3]  Nello Cristianini,et al.  An Introduction to Support Vector Machines and Other Kernel-based Learning Methods , 2000 .

[4]  Chien-Feng Huang,et al.  A hybrid stock selection model using genetic algorithms and support vector regression , 2012, Appl. Soft Comput..

[5]  Ingoo Han,et al.  Genetic algorithms approach to feature discretization in artificial neural networks for the prediction of stock price index , 2000 .

[6]  Johan A. K. Suykens,et al.  Financial time series prediction using least squares support vector machines within the evidence framework , 2001, IEEE Trans. Neural Networks.

[7]  James T. Kwok,et al.  The evidence framework applied to support vector machines , 2000, IEEE Trans. Neural Networks Learn. Syst..

[8]  Bernhard Schölkopf,et al.  A tutorial on support vector regression , 2004, Stat. Comput..

[9]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[10]  S. Sathiya Keerthi,et al.  Evaluation of simple performance measures for tuning SVM hyperparameters , 2003, Neurocomputing.

[11]  Wu Meng,et al.  Application of Support Vector Machines in Financial Time Series Forecasting , 2007 .

[12]  Dongsong Zhang,et al.  Discovering golden nuggets: data mining in financial application , 2004, IEEE Trans. Syst. Man Cybern. Part C.

[13]  Lai-Wan Chan,et al.  Support Vector Machine Regression for Volatile Stock Market Prediction , 2002, IDEAL.

[14]  Sung-Kwun Oh,et al.  Genetically optimized fuzzy polynomial neural networks , 2006, IEEE Transactions on Fuzzy Systems.

[15]  Francis Eng Hock Tay,et al.  Financial Forecasting Using Support Vector Machines , 2001, Neural Computing & Applications.

[16]  Francis Eng Hock Tay,et al.  Support vector machine with adaptive parameters in financial time series forecasting , 2003, IEEE Trans. Neural Networks.

[17]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

[18]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[19]  Sayan Mukherjee,et al.  Choosing Multiple Parameters for Support Vector Machines , 2002, Machine Learning.

[20]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[21]  Guoqiang Peter Zhang,et al.  Trend Time–Series Modeling and Forecasting With Neural Networks , 2008, IEEE Transactions on Neural Networks.

[22]  Mingcang Zhu,et al.  Housing price forecasting based on genetic algorithm and support vector machine , 2011, Expert Syst. Appl..

[23]  Mehmet Emre Çek,et al.  Analysis of observed chaotic data , 2004 .

[24]  Shie-Jue Lee,et al.  A multiple-kernel support vector regression approach for stock market price forecasting , 2011, Expert Syst. Appl..

[25]  R. H. Myers,et al.  Probability and Statistics for Engineers and Scientists , 1978 .

[26]  Birsen Eygi Erdoğan,et al.  Introduction to Probability and Statistics for Engineers and Scientist , 2014 .

[27]  F. Pérez-Cruz,et al.  Estimating GARCH models using support vector machines , 2003 .

[28]  Wei-Chiang Hong,et al.  SVR with hybrid chaotic genetic algorithms for tourism demand forecasting , 2011, Appl. Soft Comput..

[29]  Chih-Feng Liu,et al.  Application of type-2 neuro-fuzzy modeling in stock price prediction , 2012, Appl. Soft Comput..

[30]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[31]  Byung Ro Moon,et al.  A Hybrid Neurogenetic Approach for Stock Forecasting , 2007, IEEE Transactions on Neural Networks.

[32]  Shian-Chang Huang,et al.  Chaos-based support vector regressions for exchange rate forecasting , 2010, Expert Syst. Appl..

[33]  Kyoung-jae Kim,et al.  Financial time series forecasting using support vector machines , 2003, Neurocomputing.

[34]  Chuntian Cheng,et al.  Optimizing Hydropower Reservoir Operation Using Hybrid Genetic Algorithm and Chaos , 2008 .

[35]  Xin-She Yang,et al.  Nature-Inspired Metaheuristic Algorithms , 2008 .

[36]  Valeriy V. Gavrishchaka,et al.  Support Vector Machine as an Efficient Framework for Stock Market Volatility Forecasting , 2006, Comput. Manag. Sci..

[37]  Kin Keung Lai,et al.  A neural-network-based nonlinear metamodeling approach to financial time series forecasting , 2009, Appl. Soft Comput..

[38]  Mohammad Hossein Fazel Zarandi,et al.  A type-2 fuzzy rule-based expert system model for stock price analysis , 2009, Expert Syst. Appl..

[39]  Ping-Feng Pai,et al.  A hybrid ARIMA and support vector machines model in stock price forecasting , 2005 .

[40]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[41]  Lijuan Cao,et al.  Bond rating using support vector machine , 2006, Intell. Data Anal..

[42]  T. Bollerslev,et al.  Generalized autoregressive conditional heteroskedasticity , 1986 .