Forecasting stock volatility process using improved least square support vector machine approach

  • Xiao-Li Gong
  • Xi-Hua LiuEmail author
  • Xiong Xiong
  • Xin-Tian Zhuang
Methodologies and Application


Considering that the stock returns distribution displays leptokurtosis as well as left-skewed properties, and the returns volatility process exhibits heteroscedasticity as well as clustering effects, the asymmetric GARCH-type models with non-Gaussian distributions (AGARCH-nG) are employed to describe the volatility process. In addition, the AGARCH-nG models are hybridized with artificial neural network (ANN) technique for forecasting stock returns volatility. Since the least square support vector machine (LS-SVM) technique displays strong forecast ability, we present an improved particle swarm optimization (IPSO) algorithm to optimize the parameters of LS-SVM technique in the process of stock returns volatility prediction. Then, we compare the forecasting performances of individual AGARCH-nG models, the hybrid AGARCH-nG-ANN methods and the data mining-based LS-SVM-IPSO method using stock markets data. The empirical results verify the effectiveness and superiority of the proposed method, which demonstrates that the LS-SVM-IPSO approach outperforms the AGARCH-type models with non-Gaussian distributions and those integrating with the artificial neural network methods.


Stock volatility forecasting Leptokurtosis distribution Artificial neural network Least square support vector machine Particle swarm optimization algorithm 



We would like to acknowledge the financial support from the National Social Science Foundation of China (No. 18BGL200), the National Natural Science Foundation of China (No. 71532009), Research funding of Qingdao University (No. 41118010080).

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest.

Human and animals rights

This article does not contain any studies with human participants or animals performed by any of the authors.


  1. Abounoori E, Elmi Z, Nademi Y (2016) Forecasting Tehran stock exchange volatility; Markov switching GARCH approach. Phys A 445:264–282MathSciNetCrossRefGoogle Scholar
  2. Abualigah LM, Khader AT (2017) Unsupervised text feature selection technique based on hybrid particle swarm optimization algorithm with genetic operators for the text clustering. J Supercomput 73(11):4773–4795CrossRefGoogle Scholar
  3. Abualigah LM, Khader AT, Hanandeh ES (2018) A new feature selection method to improve the document clustering using particle swarm optimization algorithm. J Comput Sci 25:456–466CrossRefGoogle Scholar
  4. Alberg D, Shalit H, Yosef R (2008) Estimating stock market volatility using asymmetric GARCH models. Appl Financ Econ 18:1201–1208CrossRefGoogle Scholar
  5. Bentes SR (2015a) A comparative analysis of the predictive power of implied volatility indices and GARCH forecasted volatility. Phys A 424:105–112CrossRefGoogle Scholar
  6. Bentes SR (2015b) Forecasting volatility in gold returns under the GARCH, IGARCH and FIGARCH frameworks: new evidence. Phys A 424:355–364CrossRefGoogle Scholar
  7. Bildirici M, Ersin ÖÖ (2009) Improving forecasts of GARCH family models with the artificial neural networks: an application to the daily returns in Istanbul Stock Exchange. Expert Syst Appl 36:7355–7362CrossRefGoogle Scholar
  8. Bollerslev T (1986) Generalized heteroskedastic time series model for speculative prices and rates of return. Rev Econ Stat 69:542–547CrossRefGoogle Scholar
  9. Cheng CH, Wei LY (2009) Volatility model based on multi-stock index for TAIEX forecasting. Expert Syst Appl 36:6187–6191CrossRefGoogle Scholar
  10. Choudhary MA, Haider A (2012) Neural network models for inflation forecasting: an appraisal. Appl Econ 44:2631–2635CrossRefGoogle Scholar
  11. Chuang IY, Lu JR, Lee PH (2007) Forecasting volatility in the financial markets: a comparison of alternative distributional assumptions. Appl Financ Econ 17:1051–1060CrossRefGoogle Scholar
  12. Dai Q, Ma Z, Xie QY (2014) A two-phased and ensemble scheme integrated backpropagation algorithm. Appl Soft Comput 24:1124–1135CrossRefGoogle Scholar
  13. Dhamija AK, Bhalla VK (2010) Financial time series forecasting: comparison of neural networks and ARCH models. Int Res J Finance Econ 49:185–202Google Scholar
  14. Fang F, Jonsson H, Oosterlee K, Schoutens W (2010) Fast valuation and calibration of credit default swaps under Lévy dynamics. J Comput Finance 14:57–86MathSciNetCrossRefGoogle Scholar
  15. Göçken M, Özçalici M, Boru A, Dosdoğru AT (2016) Integrating metaheuristics and Artificial Neural Networks for improved stock price prediction. Expert Syst Appl 44:320–331CrossRefGoogle Scholar
  16. Hajizadeh E, Seifi A, Fazel MH, Zarandi Turksen IB (2012) A hybrid modeling approach for forecasting the volatility of S&P 500 index return. Expert Syst Appl 39:431–436CrossRefGoogle Scholar
  17. Ince H, Cebeci AF, Imamoglu SZ (2017) An artificial neural network-based approach to the monetary model of exchange rate. Comput Econ 2:1–15Google Scholar
  18. Ismail S, Shabri A, Samsudin R (2011) A hybrid model of self-organizing maps (SOM) and least square support vector machine (LSSVM) for time series forecasting. Expert Syst Appl 38:10574–10578CrossRefGoogle Scholar
  19. Kristjanpoller W, Minutolo MC (2016) Forecasting volatility of oil price using an artificial neural network-GARCH model. Expert Syst Appl 65:233–241CrossRefGoogle Scholar
  20. Kristjanpoller W, Fadic A, Minutolo MC (2014) Volatility forecast using hybrid Neural Network models. Expert Syst Appl 41:2437–2442CrossRefGoogle Scholar
  21. Lahmiri S (2016a) Interest rate next-day variation prediction based on hybrid feedforward neural network, particle swarm optimization, and multiresolution techniques. Phys A 444:388–396MathSciNetCrossRefGoogle Scholar
  22. Lahmiri S (2016b) A variational mode decompoisition approach for analysis and forecasting of economic and financial time series. Expert Syst Appl 55:268–273CrossRefGoogle Scholar
  23. Lahmiri S (2017) Modeling and predicting historical volatility in exchange rate markets. Phys A 471:387–395CrossRefGoogle Scholar
  24. Liu F, Zhou ZG (2015) A new data classification method based on chaotic particle swarm optimization and least square-support vector machine. Chem Intel Lab Syst 147:147–156CrossRefGoogle Scholar
  25. Lv XD, Shan X (2013) Modeling natural gas market volatility using GARCH with different distributions. Phys A 392:5685–5699CrossRefGoogle Scholar
  26. Monfared SA, Enke D (2015) Noise canceling in volatility forecasting using an adaptive neural network filter. Procedia Comput Sci 61:80–84CrossRefGoogle Scholar
  27. Nelson DB (1991) Conditional heteroskedasticity in asset returns: a new approach. Econometrica 59:347–370MathSciNetCrossRefzbMATHGoogle Scholar
  28. Pehlivanoglu YV (2013) A new particle swarm optimization method enhanced with a periodic mutation strategy and neural networks. IEEE Trans Evolut Comput 17:436–452CrossRefGoogle Scholar
  29. Qiu M, Song Y, Akagi F (2016) Application of artificial neural network for the prediction of stock market returns: the case of the Japanese stock market. Chaos Sol Fract 85:1–7MathSciNetCrossRefGoogle Scholar
  30. Ramyar S, Kianfar F (2017) Forecasting crude oil prices: a comparison between artificial neural networks and vector autoregressive models. Comput Econ 1:1–19Google Scholar
  31. Rojo-Álvarez JL, Martínez-Ramón M, Muñoz-Marí J, Camps-Valls G (2014) A unified SVM framework for signal estimation. Digital Sign Proc 26:1–20CrossRefGoogle Scholar
  32. Suykens JAK, Gestel TV, Brabanter JD, Moor BD, Vandewalle J (2002) Least square support vector machines. World Scientific, SingaporeCrossRefzbMATHGoogle Scholar
  33. Tseng CH, Cheng ST, Wang YH (2009) New hybrid methodology for stock volatility prediction. Expert Syst Appl 36:1833–1839CrossRefGoogle Scholar
  34. Yang S, Lee J (2012) Multi-basin particle swarm intelligence method for optimal calibration of parametric Lévy models. Expert Syst Appl 39:482–493CrossRefGoogle Scholar
  35. Zahedi J, Rounaghi MM (2015) Application of artificial neural network models and principal component analysis method in predicting stock prices on Tehran Stock Exchange. Phys A 438:178–187MathSciNetCrossRefGoogle Scholar
  36. Zhao J, Yang ZJ, Xu YT (2016) Nonparallel least square support vector machine for classification. Appl Intel 45:1119–1128CrossRefGoogle Scholar
  37. Zhao D, Huang C, Wei Y, Yu F, Wang M, Chen H (2017) An effective computational model for bankruptcy prediction using kernel extreme learning machine approach. Comput Econ 49:325–341CrossRefGoogle Scholar
  38. Zhu DM, Galbraith JW (2010) A generalized asymmetric Student-t distribution with application to financial econometrics. J Econometrics 157:297–305MathSciNetCrossRefzbMATHGoogle Scholar
  39. Zhu DM, Galbraith JW (2011) Modeling and forecasting expected shortfall with the generalized asymmetric Student-t and asymmetric exponential power distributions. J Emp Finance 18:765–778CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Xiao-Li Gong
    • 1
  • Xi-Hua Liu
    • 1
    Email author
  • Xiong Xiong
    • 2
    • 3
  • Xin-Tian Zhuang
    • 4
  1. 1.School of EconomicsQingdao UniversityQingdaoChina
  2. 2.College of Management and EconomicsTianjin UniversityTianjinChina
  3. 3.China Center for Social Computing and AnalyticsTianjinChina
  4. 4.School of Business AdministrationNortheastern UniversityShenyangChina

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