Abstract
Accurate financial time series forecasting is important in financial markets. However, for financial time series with low fluctuation, there is an unusual forecasting phenomenon in the popular recurrent network model forecasting, with the predictive value lagging the truth value. We call this phenomenon the lagging problem. This study proposes new evaluation measures for assessing the lagging problem, including lagging relative error, lagging value error, and lagging trend error. Moreover, the state analysis method and linear fitting model are developed to explain the causes of the lagging problem. Experimental results show that all popular recurrent network models adopted suffer from the lagging problem. This problem is caused by the failure of the nonlinear function in the prediction model and the linear degeneration of the prediction model thereafter, resulting in the suppression of the nonlinear fitting ability.
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References
Yolcu U, Egrioglu E, Aladag CH (2013) A new linear & nonlinear artificial neural network model for time series forecasting. Decis Support Syst 54(3):1340–1347. https://doi.org/10.1016/j.dss.2012.12.006
Parida A, Bisoi R, Dash P (2016) Chebyshev polynomial functions based locally recurrent neuro-fuzzy information system for prediction of financial and energy market data. J Financ Data Sci 2(3):202–223. https://doi.org/10.1016/j.jfds.2016.10.001
Cheng C-H, Yang J-H (2018) Fuzzy time-series model based on rough set rule induction for forecasting stock price. Neurocomputing 302:33–45. https://doi.org/10.1016/j.neucom.2018.04.014
Shen Z, Wang W, Shen Q et al (2020) A novel learning method for multi-intersections aware traffic flow forecasting. Neurocomputing 398:477–484. https://doi.org/10.1016/j.neucom.2019.04.094
Contreras-Reyes JE, Idrovo-Aguirre BJ (2020) Backcasting and forecasting time series using detrended cross-correlation analysis. Phys A Stat Mech Appl 560:125109. https://doi.org/10.1016/j.physa.2020.125109
LeCun Y, Bengio Y, Hinton G (2015) Deep learning nature 521(7553):436–444. https://doi.org/10.1038/nature14539
Sezer OB, Gudelek MU, Ozbayoglu AM (2020) Financial time series forecasting with deep learning: a systematic literature review. Appl Soft Comput 90:106181. https://doi.org/10.1016/j.asoc.2020.106181
Chong E, Han C, Park FC (2017) Deep learning networks for stock market analysis and prediction: methodology, data representations, and case studies. Expert Syst Appl 83:187–205. https://doi.org/10.1016/j.eswa.2017.04.030
Hiransha M, Gopalakrishnan EA, Menon VK et al (2018) NSE stock market prediction using deep-learning models. Procedia Comput Sci 132:1351–1362. https://doi.org/10.1016/j.procs.2018.05.050
Jeong G, Kim HY (2019) Improving financial trading decisions using deep Q-learning: predicting the number of shares, action strategies, and transfer learning. Expert Syst Appl 117:125–138. https://doi.org/10.1016/j.eswa.2018.09.036
Chen W, Yeo CK, Lau CT et al (2018) Leveraging social media news to predict stock index movement using RNN-boost. Data Knowl Eng 118:14–24. https://doi.org/10.1016/j.datak.2018.08.003
Deng Y, Bao F, Kong Y et al (2016) Deep direct reinforcement learning for financial signal representation and trading. IEEE Trans Neural Netw Learn Syst 28(3):653–664. https://doi.org/10.1109/TNNLS.2016.2522401
Wang B, Wang J (2019) Energy futures prices forecasting by novel DPFWR neural network and DS-CID evaluation. Neurocomputing 338:1–15. https://doi.org/10.1016/j.neucom.2019.01.092
Baffour AA, Feng J, Taylor EK (2019) A hybrid artificial neural network-GJR modeling approach to forecasting currency exchange rate volatility. Neurocomputing 365:285–301. https://doi.org/10.1016/j.neucom.2019.07.088
Sherstinsky A (2020) Fundamentals of recurrent neural network (RNN) and long short-term memory (LSTM) network. Phys D: Nonlinear Phenom 404:132306. https://doi.org/10.1016/j.physd.2019.132306
Shen G, Tan Q, Zhang H et al (2018) Deep learning with gated recurrent unit networks for financial sequence predictions. Procedia Comput Sci 131:895–903. https://doi.org/10.1016/j.procs.2018.04.298
Bengio Y, Simard P, Frasconi P (1994) Learning long-term dependencies with gradient descent is difficult. IEEE Trans Neural Netw 5(2):157–166. https://doi.org/10.1109/72.279181
Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9(8):1735–1780. https://doi.org/10.1162/neco.1997.9.8.1735
Graves A (2013) Generating sequences with recurrent neural networks. arXiv preprint arXiv:1308.0850. doi:https://doi.org/10.48550/arXiv.1308.0850
Cho K, Van Merriënboer B, Bahdanau D et al (2014) On the properties of neural machine translation: encoder–decoder approaches. arXiv preprint arXiv:1409.1259. doi:https://doi.org/10.48550/arXiv.1409.1259
Chung J, Gulcehre C, Cho K et al (2014) Empirical evaluation of gated recurrent neural networks on sequence modeling. arXiv preprint arXiv:1412.3555. doi:https://doi.org/10.48550/arXiv.1412.3555
Berradi Z, Lazaar M (2018) Integration of principal component analysis and recurrent neural network to forecast the stock price of casablanca stock exchange. In: 2nd International Conference on Intelligent Computing in Data Sciences (ICDS), pp 55–61. doi:https://doi.org/10.1016/j.procs.2019.01.008
Lu ZC, Long W, Guo Y (2018) Extreme market prediction for trading signal with deep recurrent neural network. In: 18th International Conference on Computational Science (ICCS), pp 410–418. doi:https://doi.org/10.1007/978-3-319-93701-4_31
Dixon M (2018) Sequence classification of the limit order book using recurrent neural networks. J Comput Sci 24:277–286. https://doi.org/10.1016/j.jocs.2017.08.018
Yeung J, Wei ZK, Chan KY et al (2020) Jump detection in financial time series usingmachine learning algorithms. Soft Comput 24(3):1789–1801. https://doi.org/10.1007/s00500-019-04006-2
Co NT, Son HH, Hoang NT et al (2020) Comparison between ARIMA and LSTM-RNN for VN-index prediction. In: 3rd International Conference on Intelligent Human Systems Integration (IHSI) - Integrating People and Intelligent Systems, pp 1107–1112. doi:https://doi.org/10.1007/978-3-030-39512-4_168
Sutradhar K, Sutradhar S, Jhimel IA et al (2021) Stock market prediction using recurrent neural network’s LSTM architecture. In: 12th IEEE Annual Ubiquitous Computing, Electronics and Mobile Communication Conference (UEMCON), pp 541–547. doi:https://doi.org/10.1109/uemcon53757.2021.9666562
Assaf O, Di Fatta G, Nicosia G (2021) Multivariate LSTM for stock market volatility prediction. In: 7th International Conference on Machine Learning, Optimization, and Data Science (LOD) / 1st Symposium on Artificial Intelligence and Neuroscience (ACAIN), pp 531–544. doi:https://doi.org/10.1007/978-3-030-95470-3_40
Kumar R, Kumar P, Kumar Y et al (2021) Analysis of financial time series forecasting using deep learning model. In: 11th International Conference on Cloud Computing, Data Science and Engineering (Confluence), pp 877–881. doi:https://doi.org/10.1109/Confluence51648.2021.9377158
Li JM, Wang J (2020) Forcasting of energy futures market and synchronization based on stochastic gated recurrent unit model. Energy. https://doi.org/10.1016/j.energy.2020.118787
Ungureanu S, Topa V, Cziker AC (2021) Analysis for non-residential short-term load forecasting using machine learning and statistical methods with financial impact on the power market. Energies 14(21):6966. https://doi.org/10.3390/en14216966
Touzani Y, Douzi K (2021) An LSTM and GRU based trading strategy adapted to the Moroccan market. J Big Data. https://doi.org/10.1186/s40537-021-00512-z
Alqahtani AS, Kshirsagar PR, Manoharan H et al (2022) Prophetic energy assessment with smart implements in hydroelectricity entities using artificial intelligence algorithm. Int Trans Electr Energy Syst. https://doi.org/10.1155/2022/2376353
Yan X, Wang WH, Chang M (2021) Research on financial assets transaction prediction model based on LSTM neural network. Neural Comput Appl 33(1):257–270. https://doi.org/10.1007/s00521-020-04992-7
Banerjee T, Sinha S, Choudhury P (2022) Long term and short term forecasting of horticultural produce based on the LSTM network model. Appl Intell 52(8):9117–9147. https://doi.org/10.1007/s10489-021-02845-x
Yang C, Guo SH (2021) Inflation prediction method based on deep learning. Comput Intell Neurosci. https://doi.org/10.1155/2021/1071145
Gupta U, Bhattacharjee V, Bishnu PS (2022) StockNet-GRU based stock index prediction. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2022.117986
Nelson CR, Plosser CR (1982) Trends and random walks in macroeconmic time series: some evidence and implications. J Monet Econ 10(2):139–162. https://doi.org/10.1016/0304-3932(82)90012-5
Sagheer A, Kotb M (2019) Time series forecasting of petroleum production using deep LSTM recurrent networks. Neurocomputing 323:203–213. https://doi.org/10.1016/j.neucom.2018.09.082
Lin YF, Huang TM, Chung WH et al (2021) Forecasting fluctuations in the financial index using a recurrent neural network based on price features. IEEE Trans Emerg Top Comput Intell 5(5):780–791. https://doi.org/10.1109/tetci.2020.2971218
Wang L, Gupta S (2013) Neural networks and wavelet de-noising for stock trading and prediction. In: Pedrycz W, Chen S-M (eds) Time series analysis, modeling and applications: a computational intelligence perspective. Springer Berlin Heidelberg, Berlin, Heidelberg, pp 229–247. https://doi.org/10.1007/978-3-642-33439-9_11
Hajiabotorabi Z, Kazemi A, Samavati FF et al (2019) Improving DWT-RNN model via B-spline wavelet multiresolution to forecast a high-frequency time series. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2019.112842
Yan H, Ouyang H (2018) Financial time series prediction based on deep learning. Wirel Pers Commun 102(2):683–700. https://doi.org/10.1007/s11277-017-5086-2
Huang NE, Shen Z, Long SR et al (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc Royal Soc a-Math Phys Eng Sci 454(1971):903–995. https://doi.org/10.1098/rspa.1998.0193
Wu Z, Huang NE (2009) Ensemble empirical mode decomposition: a noise-assisted data analysis method. Adv Adapt Data Anal 1(01):1–41. https://doi.org/10.1142/S1793536909000047
Torres ME, Colominas MA, Schlotthauer G et al (2011) A complete ensemble empirical mode decomposition with adaptive noise. In: 2011 IEEE international conference on acoustics, speech and signal processing (ICASSP), pp 4144–4147. doi:https://doi.org/10.1109/ICASSP.2011.5947265
He J (2021) Application of deep learning model under improved emd in railway transportation investment benefits and national economic attribute analysis. J Supercomput 77(8):8194–8208. https://doi.org/10.1007/s11227-020-03609-z
Lin HL, Sun QB (2020) Crude oil prices forecasting: an approach of using CEEMDAN-based multi-layer gated recurrent unit networks. Energies. https://doi.org/10.3390/en13071543
Yang M, Wang J (2022) Adaptability of financial time series prediction based on BiLSTM. Procedia Comput Sci 199:18–25. https://doi.org/10.1016/j.procs.2022.01.003
Akbar SB, Thanupillai K, Govindarajan V (2022) Forecasting Bitcoin price using time opinion mining and bi-directional GRU. J Intell Fuzzy Syst 42(3):1825–1833. https://doi.org/10.3233/jifs-211217
Hyndman RJ, Koehler AB (2006) Another look at measures of forecast accuracy. Int J Forecast 22(4):679–688. https://doi.org/10.1016/j.ijforecast.2006.03.001
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Li, J., Song, L., Wu, D. et al. Lagging problem in financial time series forecasting. Neural Comput & Applic 35, 20819–20839 (2023). https://doi.org/10.1007/s00521-023-08879-1
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DOI: https://doi.org/10.1007/s00521-023-08879-1