Deep learning stacking for financial time series forecasting: an analysis with synthetic and real-world time series

  • Eder F. Urbinate USP
  • Leonardo K. Felizardo USP
  • Emilio Del-Moral-Hernandez USP


The forecasting problem is one of the main applications arising from the synergy between finance and artificial intelligence. With the advancement in the field of deep learning, some ANN achieved very satisfactory results and gained more attention. One approach to increase the time series forecasting model’s performance is ensemble models, combining each model’s prediction (stacking). However, there are some difficulties in combining and evaluating these models for a good performance in financial time series. We use synthetic and real-world time series to evaluate the model stacking, trying to understand the main financial time series components. Using this ensemble method, we reduced the prediction error for both scenarios.


Akyol, K. (2020). Stacking ensemble based deep neural networks modeling for effective epileptic seizure detection. Expert Systems with Applications, 148:113239.

Cheng, H., Tan, P.-N., Gao, J., and Scripps, J. (2006). Multistep-ahead time series prediction. In Pacific-Asia Conference on Knowledge Discovery and Data Mining, pages 765-774. Springer.

Di Persio, L. and Honchar, O. (2016). Artificial neural networks architectures for stock price prediction: Comparisons and applications. International Journal of Circuits, Systems and Signal Processing, 10(2016):403-413.

Dieker, A. and Mandjes, M. (2003). On spectral simulation of fractional brownian motion. Probability in the Engineering and Informational Sciences, 17(3):417-434.

Dietterich, T. G. (2000). Ensemble methods in machine learning. In Multiple Classifier Systems, pages 1-15, Berlin, Heidelberg. Springer Berlin Heidelberg.

He, K., Zhang, X., Ren, S., and Sun, J. (2016). Deep residual learning for image recognition. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

Hochreiter, S. and Schmidhuber, J. (1997). Long Short-Term Memory. Neural Computation, 9(8):1735-1780.

Hu, Z., Zhao, Y., and Khushi, M. (2021). A survey of forex and stock price prediction using deep learning. Applied System Innovation, 4(1).

Ibrahim, S. N. I., Misiran, M., and Laham, M. F. (2021). Geometric fractional brownian motion model for commodity market simulation. Alexandria Engineering Journal, 60(1):955-962.

Imperial, F. and Segura, A. S. (2018). Modelling Stock Prices and Stock Market Behaviour using the Irrational Fractional Brownian Motion: An Application to the S&P500 in Eight Different Periods. PhD thesis, PhD thesis, June.

Ismail Fawaz, H., Forestier, G., Weber, J., Idoumghar, L., and Muller, P. A. (2019). Deep learning for time series classification: a review. Data Mining and Knowledge Discovery.

Jin, Y., Okabe, T., and Sendhoff, B. (2004). Neural network regularization and ensembling using multi-objective evolutionary algorithms. In Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753), volume 1, pages 1-8 Vol.1.

Krizhevsky, A., Sutskever, I., and Hinton, G. E. (2012). Imagenet classification with deep convolutional neural networks. Advances in neural information processing systems, 25:1097-1105.

Lim, B. and Zohren, S. (2021). Time-series forecasting with deep learning: a survey. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 379(2194):20200209.

Mandelbrot, B. B. and Van Ness, J. W. (1968). Fractional brownian motions, fractional noises and applications. SIAM Review, 10(4):422-437.

Maqsood, I., Khan, M. R., and Abraham, A. (2004). An ensemble of neural networks for weather forecasting. Neural Computing & Applications, 13(2):112-122.

Mehtab, S., Sen, J., and Dasgupta, S. (2020). Robust analysis of stock price time series using cnn and lstm-based deep learning models. In 2020 4th International Conference on Electronics, Communication and Aerospace Technology (ICECA), pages 1481-1486.

Osborne, M. F. (1959). Brownian motion in the stock market. Operations research, 7(2):145-173.

Pérez-Ortiz, J. A., Schmidhuber, J., Gers, F. A., and Eck, D. (2002). Improving long-term online prediction with decoupled extended kalman filters. In International Conference on Artificial Neural Networks, pages 1055-1060. Springer.

Sagheer, A. and Kotb, M. (2019). Time series forecasting of petroleum production using deep lstm recurrent networks. Neurocomputing, 323:203-213.

Selvin, S., Vinayakumar, R., Gopalakrishnan, E. A., Menon, V. K., and Soman, K. P. (2017). Stock price prediction using lstm, rnn and cnn-sliding window model. In 2017 International Conference on Advances in Computing, Communications and Informatics (ICACCI), pages 1643-1647.

Sezer, O. B., Gudelek, M. U., and Ozbayoglu, A. M. (2020). Financial time series forecasting with deep learning: A systematic literature review: 2005-2019. Applied Soft Computing Journal.

Waheeb, W., Ghazali, R., and Shah, H. (2019). Nonlinear autoregressive moving-average (narma) time series forecasting using neural networks. In 2019 International Conference on Computer and Information Sciences (ICCIS), pages 1-5.

Wang, K., Li, K., Zhou, L., Hu, Y., Cheng, Z., Liu, J., and Chen, C. (2019). Multiple convolutional neural networks for multivariate time series prediction. Neurocomputing.

Yang, J. B., Nguyen, M. N., San, P. P., Li, X. L., and Krishnaswamy, S. (2015). Deep convolutional neural networks on multichannel time series for human activity recognition. In IJCAI International Joint Conference on Artificial Intelligence.

Zheng, Y., Liu, Q., Chen, E., Ge, Y., and Zhao, J. L. (2014). Time series classification using multi-channels deep convolutional neural networks. In Li, F., Li, G., Hwang, S.-w., Yao, B., and Zhang, Z., editors, Web-Age Information Management, pages 298-310, Cham. Springer International Publishing.
URBINATE, Eder F.; FELIZARDO, Leonardo K.; DEL-MORAL-HERNANDEZ, Emilio. Deep learning stacking for financial time series forecasting: an analysis with synthetic and real-world time series. In: ENCONTRO NACIONAL DE INTELIGÊNCIA ARTIFICIAL E COMPUTACIONAL (ENIAC), 19. , 2022, Campinas/SP. Anais [...]. Porto Alegre: Sociedade Brasileira de Computação, 2022 . p. 106-117. ISSN 2763-9061. DOI: