{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T06:16:04Z","timestamp":1778220964397,"version":"3.51.4"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,19]],"date-time":"2022-01-19T00:00:00Z","timestamp":1642550400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62067001"],"award-info":[{"award-number":["62067001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004607","name":"Guangxi Natural Science Foundation","doi-asserted-by":"publisher","award":["2019JJA170045"],"award-info":[{"award-number":["2019JJA170045"]}],"id":[{"id":"10.13039\/501100004607","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Special Funds for Guangxi BaGui Scholars","award":["Jia Xu"],"award-info":[{"award-number":["Jia Xu"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The stock index is an important indicator to measure stock market fluctuation, with a guiding role for investors\u2019 decision-making, thus being the object of much research. However, the stock market is affected by uncertainty and volatility, making accurate prediction a challenging task. We propose a new stock index forecasting model based on time series decomposition and a hybrid model. Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) decomposes the stock index into a series of Intrinsic Mode Functions (IMFs) with different feature scales and trend term. The Augmented Dickey Fuller (ADF) method judges the stability of each IMFs and trend term. The Autoregressive Moving Average (ARMA) model is used on stationary time series, and a Long Short-Term Memory (LSTM) model extracts abstract features of unstable time series. The predicted results of each time sequence are reconstructed to obtain the final predicted value. Experiments are conducted on four stock index time series, and the results show that the prediction of the proposed model is closer to the real value than that of seven reference models, and has a good quantitative investment reference value.<\/jats:p>","DOI":"10.3390\/e24020146","type":"journal-article","created":{"date-parts":[[2022,1,19]],"date-time":"2022-01-19T08:20:57Z","timestamp":1642580457000},"page":"146","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":45,"title":["Stock Index Prediction Based on Time Series Decomposition and Hybrid Model"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3425-9913","authenticated-orcid":false,"given":"Pin","family":"Lv","sequence":"first","affiliation":[{"name":"School of Computer, Electronics and Information, Guangxi University, Nanning 530004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qinjuan","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Computer, Electronics and Information, Guangxi University, Nanning 530004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4061-8262","authenticated-orcid":false,"given":"Jia","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Computer, Electronics and Information, Guangxi University, Nanning 530004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8743-8993","authenticated-orcid":false,"given":"Yating","family":"Shu","sequence":"additional","affiliation":[{"name":"School of Computer, Electronics and Information, Guangxi University, Nanning 530004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"113609","DOI":"10.1016\/j.eswa.2020.113609","article-title":"A novel deep learning framework: Prediction and analysis of financial time series using CEEMD and LSTM","volume":"159","author":"Yan","year":"2020","journal-title":"Expert Syst. Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.eswa.2018.07.065","article-title":"EMD2FNN: A strategy combining empirical mode decomposition and factorization machine based neural network for stock market trend prediction","volume":"115","author":"Zhou","year":"2019","journal-title":"Expert Syst. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Torres, M.E., Colominas, M.A., Schlotthauer, G., and Flandrin, P. (2011, January 22\u201327). A complete ensemble empirical mode decomposition with adaptive noise. Proceedings of the 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic.","DOI":"10.1109\/ICASSP.2011.5947265"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.neucom.2019.05.099","article-title":"Improving forecasting accuracy of time series data using a new ARIMA-ANN hybrid method and empirical mode decomposition","volume":"361","author":"Ertekin","year":"2019","journal-title":"Neurocomputing"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Wang, Z., and Lou, Y. (2019, January 15\u201317). Hydrological time series forecast model based on wavelet de-noising and ARIMA-LSTM. Proceedings of the 2019 IEEE 3rd Information Technology, Networking, Electronic and Automation Control Conference (ITNEC), Chengdu, China.","DOI":"10.1109\/ITNEC.2019.8729441"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.asoc.2014.05.028","article-title":"A moving-average filter based hybrid ARIMA\u2013ANN model for forecasting time series data","volume":"23","author":"Babu","year":"2014","journal-title":"Appl. Soft Comput."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.physa.2018.11.061","article-title":"Financial time series forecasting model based on CEEMDAN and LSTM","volume":"519","author":"Cao","year":"2019","journal-title":"Phys. Stat. Mech. Its Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2664","DOI":"10.1016\/j.asoc.2010.10.015","article-title":"A novel hybridization of artificial neural networks and ARIMA models for time series forecasting","volume":"11","author":"Khashei","year":"2011","journal-title":"Appl. Soft Comput."},{"key":"ref_9","unstructured":"Goodfellow, I., Bengio, Y., and Courville, A. (2016). Deep Learning, MIT Press."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Gers, F.A., Eck, D., and Schmidhuber, J. (2002). Applying LSTM to time series predictable through time-window approaches. Neural Nets WIRN Vietri-01, Springer.","DOI":"10.1007\/978-1-4471-0219-9_20"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Bao, W., Yue, J., and Rao, Y. (2017). A deep learning framework for financial time series using stacked autoencoders and long-short term memory. PLoS ONE, 12.","DOI":"10.1371\/journal.pone.0180944"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Chung, H., and Shin, K.S. (2018). Genetic algorithm-optimized long short-term memory network for stock market prediction. Sustainability, 10.","DOI":"10.3390\/su10103765"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/0098-1354(92)80049-F","article-title":"Neural network forecasting of short, noisy time series","volume":"16","author":"Foster","year":"1992","journal-title":"Comput. Chem. Eng."},{"key":"ref_14","unstructured":"Brace, M.C., Schmidt, J., and Hadlin, M. (1991, January 23\u201326). Comparison of the forecasting accuracy of neural networks with other established techniques. Proceedings of the First International Forum on Applications of Neural Networks to Power Systems, Seattle, WA, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/j.omega.2004.07.024","article-title":"A hybrid ARIMA and support vector machines model in stock price forecasting","volume":"33","author":"Pai","year":"2005","journal-title":"Omega"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.eswa.2018.03.002","article-title":"Forecasting the volatility of stock price index: A hybrid model integrating LSTM with multiple GARCH-type models","volume":"103","author":"Kim","year":"2018","journal-title":"Expert Syst. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/S0925-2312(01)00702-0","article-title":"Time series forecasting using a hybrid ARIMA and neural network model","volume":"50","author":"Zhang","year":"2003","journal-title":"Neurocomputing"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1504\/IJBAAF.2014.064307","article-title":"Forecasting stock index returns using ARIMA-SVM, ARIMA-ANN, and ARIMA-random forest hybrid models","volume":"5","author":"Kumar","year":"2014","journal-title":"Int. J. Bank. Account. Financ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1098\/rspa.1998.0193","article-title":"The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis","volume":"454","author":"Huang","year":"1998","journal-title":"Proc. R. Soc. London. Ser. Math. Phys. Eng. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Song, H., Dai, J., Luo, L., Sheng, G., and Jiang, X. (2018). Power transformer operating state prediction method based on an LSTM network. Energies, 11.","DOI":"10.3390\/en11040914"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Ren, B. (2020). The use of machine translation algorithm based on residual and LSTM neural network in translation teaching. PLoS ONE, 15.","DOI":"10.1371\/journal.pone.0240663"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"113917","DOI":"10.1016\/j.enconman.2021.113917","article-title":"Application of hybrid model based on empirical mode decomposition, novel recurrent neural networks and the ARIMA to wind speed prediction","volume":"233","author":"Liu","year":"2021","journal-title":"Energy Convers. Manag."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"654","DOI":"10.1016\/j.ejor.2017.11.054","article-title":"Deep learning with long short-term memory networks for financial market predictions","volume":"270","author":"Fischer","year":"2018","journal-title":"Eur. J. Oper. Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1016\/j.eswa.2018.11.028","article-title":"Multi-output bus travel time prediction with convolutional LSTM neural network","volume":"120","author":"Petersen","year":"2019","journal-title":"Expert Syst. Appl."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.eswa.2018.04.004","article-title":"Web traffic anomaly detection using C-LSTM neural networks","volume":"106","author":"Kim","year":"2018","journal-title":"Expert Syst. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"106806","DOI":"10.1016\/j.asoc.2020.106806","article-title":"Predicting stock price trends based on financial news articles and using a novel twin support vector machine with fuzzy hyperplane","volume":"98","author":"Hao","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Wu, D., Wang, X., and Wu, S. (2021). A Hybrid Method Based on Extreme Learning Machine and Wavelet Transform Denoising for Stock Prediction. Entropy, 23.","DOI":"10.3390\/e23040440"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"746","DOI":"10.1016\/j.jmsy.2020.11.020","article-title":"Operational time-series data modeling via LSTM network integrating principal component analysis based on human experience","volume":"61","author":"Yang","year":"2020","journal-title":"J. Manuf. Syst."},{"key":"ref_29","unstructured":"Coyle, D., Prasad, G., and McGinnity, T.M. (2004, January 1\u20135). Extracting features for a brain-computer interface by self-organising fuzzy neural network-based time series prediction. Proceedings of the 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, San Francisco, CA, USA."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1016\/j.asoc.2014.06.027","article-title":"Forecasting wind speed using empirical mode decomposition and Elman neural network","volume":"23","author":"Wang","year":"2014","journal-title":"Appl. Soft Comput."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/2\/146\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:03:43Z","timestamp":1760133823000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/2\/146"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,19]]},"references-count":30,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["e24020146"],"URL":"https:\/\/doi.org\/10.3390\/e24020146","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,19]]}}}