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Deep Nonlinear Ensemble Framework for Stock Index Forecasting and Uncertainty Analysis

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Abstract

Stock index forecasting plays an important role in avoiding risk and increasing returns for financial regulators and investors. However, due to the volatility and uncertainty of the stock market, forecasting stock indices accurately is challenging. In this paper, a deep nonlinear ensemble framework is proposed for stock index forecasting and uncertainty analysis. (1) Singular spectrum analysis (SSA) is utilized to extract features from a raw stock index and eliminate the interference. (2) Enhanced weighted support vector machine (EWSVM) is proposed for forecasting each component that is decomposed, of which the penalty weights are based on the time order and the hyperparameters are optimized using the simulated annealing algorithm. (3) Recurrent neural network (RNN) is used to integrate the forecast of each component into the final point forecast. (4) Gaussian process regression (GPR) is applied to obtain the interval forecast of the original stock index. Two practical cases (Nikkei 225 Index, Japan and Hang Seng Index, Hong Kong, China) are utilized to evaluate the performance of the proposed model. In terms of the results of point forecasting, the MAE, \({R}^{2}\), MAPE, and RMSE of Nikkei 225 Index are 66.0745, 0.9972, 0.0066, and 80.0381, and those of Hang Seng Index are 79.2145,0.9968, 0.0073, and 96.7740. In terms of the results of interval forecasting, the \({CP}_{95\%}\), \({MWP}_{95\%}\), and \({MC}_{95\%}\) of Nikkei 225 Index are 0.89979, 0.05746, and 0.06385, and those of Hang Seng Index are 0.97985, 0.28223, and 0.28803. Forecasting stock indices accurately is crucial for investment decision and risk management and is extremely meaningful to investors and financial regulators. In this paper, the SSA-EWSVM-RNN-GPR model is used to forecast the closing prices of stock indices, and compared with eight benchmark models, the proposed SSA-EWSVM-RNN-GPR model can be an effective tool for both point and interval forecasting of stock indices.

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Abbreviations

ANN:

Artificial neutral network

ARMA:

Auto-regressive moving average model

BP:

Back propagation network

CP α :

Coverage probability

EMD:

Empirical mode decomposition

EWSVM:

Enhanced weighted support vector machine

GARCH:

Generalized auto-regressive conditional heteroskedasticity

GP:

Gaussian process

GPR:

Gaussian process regression

MAE:

Mean absolute error

MAPE:

Mean absolute percentage error

MC α :

MWPα Divided by CPα

MSE:

Mean square error

MWP α :

Mean width percentage

RBF:

Radial basis function

RIM:

Residual income model

RNN:

Recurrent neutral network

RMSE:

Root mean square error

R 2 :

Coefficient of determination

SAA:

Simulated annealing algorithm

SSA:

Singular spectrum analysis

SVM:

Support vector machine

SVD:

Singular value decomposition

SWLSTM:

Shared weight long short-term memory network

T-EOF:

Time-empirical orthogonal function

WD:

Wavelet decomposition

WSVM:

Weighted support vector machine

References

  1. Long W, Lu Z, Cui L. Deep learning-based feature engineering for stock price movement prediction. Knowl-Based Syst. 2019;164:163–73.

    Article  Google Scholar 

  2. Zhang K, Zhong G, Dong J, Wang S, Wang Y. Stock market prediction based on generative adversarial network. Proced Comput Sci. 2019;147:400–6.

    Article  Google Scholar 

  3. Wang Y, Wang L, Yang F, Di W, Chang Q. Advantages of direct input-to-output connections in neural networks: the Elman network for stock index forecasting. Inf Sci. 2021;547:1066–79.

    Article  MathSciNet  Google Scholar 

  4. Wafi AS, Hassan H, Mabrouk A. Fundamental analysis models in financial markets–review study. Proced Econ Financ. 2015;30:939–47.

    Article  Google Scholar 

  5. Rounaghi MM, Zadeh FN. Investigation of market efficiency and financial stability between S&P 500 and London stock exchange: monthly and yearly forecasting of time series stock returns using ARMA model. Physica A. 2016;456:10–21.

    Article  Google Scholar 

  6. Chen S, Jeong K, Härdle WK. Recurrent support vector regression for a non-linear ARMA model with applications to forecasting financial returns. Computation Stat. 2015;30(3):821–43.

    Article  MathSciNet  Google Scholar 

  7. Francq C, Wintenberger O, Zakoïan JM. Goodness-of-fit tests for Log-GARCH and EGARCH models. TEST. 2018;27(1):27–51.

    Article  MathSciNet  Google Scholar 

  8. Shi S, Liu W, Jin M. Stock price forecasting based on a combined model of ARMA and BP neural network and Markov model. J Inform Process Manage. 2013;4(3):215–21.

    Google Scholar 

  9. Wei Y, Yu Q, Liu J, Cao Y. Hot money and China’s stock market volatility: further evidence using the GARCH–MIDAS model. Physica A. 2018;492:923–30.

    Article  Google Scholar 

  10. Zhang X, Frey R. Improving ARMA-GARCH forecasts for high frequency data with regime-switching ARMA-GARCH. J Comput Anal Appl. 2015;18(1):727–51.

    MathSciNet  MATH  Google Scholar 

  11. Yu J, Tan M, Zhang H, Tao D, Rui Y. Hierarchical deep click feature prediction for fine-grained image recognition. IEEE Trans Pattern Anal Mach Intell. 2019;99:1–1.

    Google Scholar 

  12. Yu J, Tao D, Wang M, Rui Y. Learning to rank using user clicks and visual features for image retrieval. IEEE Trans Cybern. 2015;45(4):767–79.

    Article  Google Scholar 

  13. Pan Y, Xiao Z, Wang X, Yang D. A multiple support vector machine approach to stock index forecasting with mixed frequency sampling. Knowl-Based Syst. 2017;122:90–102.

    Article  Google Scholar 

  14. Wang J, Wang J. Forecasting stock market indexes using principle component analysis and stochastic time effective neural networks. Neurocomputing. 2015;156:68–78.

    Article  Google Scholar 

  15. Grigoryan H. A Stock market prediction method based on support vector machines (SVM) and independent component analysis (ICA). Database Sys J. 2016;7(1):12–21.

    MathSciNet  Google Scholar 

  16. Moghaddam AH, Moghaddam MH, Esfandyari M. Stock market index prediction using artificial neural network. Journal of Economics Financ Administr S. 2016;21(41):89–93.

    Google Scholar 

  17. Zhang D, Lou S. The application research of neural network and BP algorithm in stock price pattern classification and prediction. Future Gener Comp Sy. 2021;115:872–9.

    Article  Google Scholar 

  18. Xiao J, Zhu X, Huang C, Yang X, Wen F, Zhong M. A new approach for stock price analysis and prediction based on SSA and SVM. J Inform Techn Decis Making. 2019;18(01):287–310.

    Article  Google Scholar 

  19. Chandar SK. Hybrid models for intraday stock price forecasting based on artificial neural networks and metaheuristic algorithms. Pattern Recogn Lett. 2021;147:124–33.

    Article  Google Scholar 

  20. Chen Y, Hao Y. Integrating principle component analysis and weighted support vector machine for stock trading signals prediction. Neurocomputing. 2018;321:381–402.

    Article  Google Scholar 

  21. Huang C, Zhou J, Chen J, Yang J, Clawson K, Peng Y. A feature weighted support vector machine and artificial neural network algorithm for academic course performance prediction. Neural Comput Appl. 2021; 1–13.

  22. Fayed HA, Atiya AF. Speed up grid-search for parameter selection of support vector machines. Appl Soft Comput. 2019;80:202–10.

    Article  Google Scholar 

  23. Bergstra J, Bengio Y. Random search for hyper-parameter optimization. J Mach Learn Res. 2012;13:281–305.

    MathSciNet  MATH  Google Scholar 

  24. Tao Y, Yan H, Gao H, Sun Y, Li G. Application of SVR optimized by modified simulated annealing (MSA-SVR) air conditioning load prediction model. J Ind Inf Integr. 2019;15:247–51.

    Google Scholar 

  25. Winters-Hilt S. Clustering via support vector machine boosting with simulated annealing. Int J Comput Optim. 2017;4(1):53–89.

    Google Scholar 

  26. Gao T, Chai Y. Improving stock closing price prediction using recurrent neural network and technical indicators. Neural Computat. 2018;1–22.

  27. Qiu Y, Yang HY, Lu S, Chen W. A novel hybrid model based on recurrent neural networks for stock market timing. Soft Comput. 2020; 1–18.

  28. Wang JZ, Wang JJ, Zhang ZG, Guo SP. Forecasting stock indices with back propagation neural network. Expert Syst Appl. 2011;38(11):14346–55.

    Google Scholar 

  29. Wei LY. A hybrid ANFIS model based on empirical mode decomposition for stock time series forecasting. Appl Soft Comput. 2016;42:368–76.

    Article  Google Scholar 

  30. Ghodsi M, Hassani H, Rahmani D, Silva ES. Vector and recurrent singular spectrum analysis: which is better at forecasting. J Appl Stat. 2018;45(10):1872–99.

    Article  MathSciNet  Google Scholar 

  31. Lahmiri S. Minute-ahead stock price forecasting based on singular spectrum analysis and support vector regression. Appl Math Comput. 2018;320:444–51.

    MathSciNet  MATH  Google Scholar 

  32. Leles MC, Moreira MG, Vale-Cardoso AS, Nascimento CL, Sbruzzi EF, Guimarães HN. Comparision between Basic and Toeplitiz SSA applied to non-stationary time-series. Stat Interface. 2019;12(4):527–36.

    Article  MathSciNet  Google Scholar 

  33. Liu H, Mi X, Li Y, Duan Z, Xu Y. Smart wind speed deep learning based multi-step forecasting model using singular spectrum analysis, convolutional gated recurrent unit network and support vector regression. Renew Energ. 2019;143:842–54.

    Article  Google Scholar 

  34. Wen F, Xiao J, He Z, Gong X. Stock price prediction based on SSA and SVM. Proced Comput Sci. 2014;31:625–31.

    Article  Google Scholar 

  35. Wang J, Wang Z, Li X, Zhou H. Artificial bee colony-based combination approach to forecasting agricultural commodity prices. J Forecast. 2019; https://doi.org/10.1016/j.ijforecast.2019.08.006

  36. Bishoyi A, Wang X, Dey DK. learning semiparametric regression with missing covariates using Gaussian process models. Bayesian Anal. 2020;15(1):215–39.

    Article  MathSciNet  Google Scholar 

  37. Chandorkar M, Camporeale E, Wing S. Probabilistic forecasting of the disturbance storm time index: an autoregressive Gaussian process approach. Space Weather. 2017;15(8):1004–19.

    Article  Google Scholar 

  38. Fang D, Zhang X, Yu Q, Jin TC, Tian L. A novel method for carbon dioxide emission forecasting based on improved Gaussian processes regression. J clean Prod. 2018;173:143–50.

    Article  Google Scholar 

  39. Zhang C, Wei H, Zhao X, Liu T, Zhang K. A Gaussian process regression based hybrid approach for short-term wind speed prediction. Energ Convers Manage. 2016;126:1084–92.

    Article  Google Scholar 

  40. Zhang Z, Ye L, Qin H, Liu Y, Wang C, Yu X, et al. Wind speed prediction method using shared weight long short-term memory network and Gaussian process regression. Appl Energ. 2019;247:270–84.

    Article  Google Scholar 

  41. Liu K, Zhou J, Dong D. Improving stock price prediction using the long short-term memory model combined with online social networks. J Behav Exp Finance. 2021;30:100507.

    Article  Google Scholar 

  42. Hajiabotorabi Z, Kazemi A, Samavati FF, Ghaini FMM. Improving DWT-RNN model via B-spline wavelet multiresolution to forecast a high-frequency time series. Expert Syst Appl. 2019;138:112842.

    Article  Google Scholar 

  43. Marković I, Stojanović M, Stanković J, Stanković M. Stock market trend prediction using AHP and weighted kernel LS-SVM. Soft Comput. 2017;21(18):5387–98.

    Article  Google Scholar 

  44. Chen TT, Lee SJ. A weighted LS-SVM based learning system for time series forecasting. Inf Sci. 2015;299:99–116.

    Article  MathSciNet  Google Scholar 

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Funding

This research was supported by the National Natural Science Foundation of China (Grant No. 71971122 and 71501101).

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Authors and Affiliations

  1. School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Jujie Wang

  2. Changwang School of Honors, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Liu Feng, Yang Li & Chunchen Feng

  3. School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Junjie He

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  1. Jujie Wang
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  3. Yang Li
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Correspondence to Jujie Wang.

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Wang, J., Feng, L., Li, Y. et al. Deep Nonlinear Ensemble Framework for Stock Index Forecasting and Uncertainty Analysis. Cogn Comput 13, 1574–1592 (2021). https://doi.org/10.1007/s12559-021-09961-3

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