{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T02:19:25Z","timestamp":1789093165100,"version":"build-2803163510"},"reference-count":53,"publisher":"Public Library of Science (PLoS)","issue":"6","license":[{"start":{"date-parts":[[2025,6,2]],"date-time":"2025-06-02T00:00:00Z","timestamp":1748822400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No.72071095"],"award-info":[{"award-number":["No.72071095"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:p>LSTM (Long Short-Term Memory Network) is currently extensively utilized for forecasting financial time series, primarily due to its distinct advantages in separating the long-term from the short-term memory information within a sequence. However, the experimental results presented in this paper indicate that LSTM may struggle to clearly differentiate between these two types of information. To overcome this limitation, we propose the ARMA-RNN-LSTM Hybrid Model, aimed at enhancing the separation between the long-term and short-term memory information on top of LSTM framework. The experiment in this paper is inspired by an observation: when LSTMs and RNNs are respectively used to forecast the same time series that contains only short-term memory information, LSTMs exhibit significantly lower forecasting accuracy than RNNs, and we attributed this to LSTMs potentially misclassifying some short-term memory information as long-term during forecasting process. Further, we speculate that this confusion might also arise when LSTMs are used to forecast the time series containing both the long-term and short-term memory information. To verify the aforementioned hypothesis and improve the forecasting accuracy for financial time series, this paper combines RNNs with LSTMs, proposing a method of ARMA-RNN-LSTM Hybrid Modelling, and conducts an experiment with stock index prices. Eventually, the experiment results show that the ARMA-RNN-LSTM Hybrid Model outperforms standalone RNNs and LSTMs in forecasting stock index series containing both long-term and short-term memory information, confirming that the ARMA-RNN-LSTM Hybrid Model has effectively enhanced the separation between the long-term and short-term memory information within sequence. This hybrid modelling approach has innovatively addressed the issue of the confusion between the long-term and the short-term memory information in a sequence during LSTM\u2019s forecasting process, improving the accuracy of forecasting financial time series, and demonstrates that neural network\u2019s forecasting errors is a area worth to explore in the future.<\/jats:p>","DOI":"10.1371\/journal.pone.0322737","type":"journal-article","created":{"date-parts":[[2025,6,2]],"date-time":"2025-06-02T13:27:54Z","timestamp":1748870874000},"page":"e0322737","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":3,"title":["Enhanced separation of long-term memory from short-term memory on top of LSTM: Neural network-based stock index forecasting"],"prefix":"10.1371","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-7450-5371","authenticated-orcid":true,"given":"Hongfei","family":"Xiao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2025,6,2]]},"reference":[{"key":"pone.0322737.ref001","volume-title":"Time series and statistics","author":"M Nerlove","year":"1990"},{"key":"pone.0322737.ref002","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-031-70584-7_3","article-title":"ARIMA models","volume-title":"Time series analysis and its applications. Springer Texts in Statistics","author":"RH Shumway","year":"2025"},{"issue":"4","key":"pone.0322737.ref003","doi-asserted-by":"crossref","DOI":"10.18637\/jss.v027.i04","article-title":"VAR, SVAR and SVEC models: implementation within R package vars","volume":"27","author":"B Pfaff","year":"2008","journal-title":"J Stat Soft"},{"issue":"2","key":"pone.0322737.ref004","doi-asserted-by":"crossref","DOI":"10.3150\/bj\/1068128975","article-title":"GARCH processes: structure and estimation","volume":"9","author":"I Berkes","year":"2003","journal-title":"Bernoulli"},{"key":"pone.0322737.ref005","doi-asserted-by":"crossref","first-page":"115149","DOI":"10.1016\/j.eswa.2021.115149","article-title":"A hybrid approach of adaptive wavelet transform, long short-term memory and ARIMA-GARCH family models for the stock index prediction","volume":"182","author":"M Zolfaghari","year":"2021","journal-title":"Expert Syst Appl"},{"issue":"1","key":"pone.0322737.ref006","article-title":"The comparison among ARIMA and hybrid ARIMA-GARCH models in forecasting the exchange rate of Iran.","volume":"7","author":"M Pahlavani","year":"2015","journal-title":"Int J Bus Dev Stud"},{"issue":"3","key":"pone.0322737.ref007","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":"M Kumar","year":"2014","journal-title":"Int J Bank Account Finance"},{"key":"pone.0322737.ref008","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2020\/6622927","article-title":"A CNN-LSTM-based model to forecast stock prices","volume":"2020","author":"W Lu","year":"2020","journal-title":"Complexity"},{"key":"pone.0322737.ref009","doi-asserted-by":"crossref","first-page":"120069","DOI":"10.1016\/j.energy.2021.120069","article-title":"A novel genetic LSTM model for wind power forecast","volume":"223","author":"F Shahid","year":"2021","journal-title":"Energy"},{"key":"pone.0322737.ref010","doi-asserted-by":"crossref","first-page":"106435","DOI":"10.1016\/j.cie.2020.106435","article-title":"An optimized model using LSTM network for demand forecasting","volume":"143","author":"H Abbasimehr","year":"2020","journal-title":"Comput Ind Eng"},{"issue":"3","key":"pone.0322737.ref011","first-page":"259","article-title":"Statistical methodology for nonperiodic cycles: from the covariance to R\/S analysis","volume":"1","author":"B Mandelbrot","year":"1972","journal-title":"Ann Econ Soc Measure"},{"issue":"5","key":"pone.0322737.ref012","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pone.0127824","article-title":"The effect of the underlying distribution in Hurst exponent estimation","volume":"10","author":"M\u00c1 S\u00e1nchez","year":"2015","journal-title":"PLoS One"},{"issue":"6","key":"pone.0322737.ref013","article-title":"Multifractality approach of a generalized Shannon index in financial time series","volume":"19","author":"FS Abril-Berm\u00fadez","year":"2024","journal-title":"PLoS One"},{"issue":"6","key":"pone.0322737.ref014","article-title":"Statistical analysis of Hurst exponents of essential\/nonessential genes in 33 bacterial genomes","volume":"10","author":"X Liu","year":"2015","journal-title":"PLoS One"},{"issue":"1","key":"pone.0322737.ref015","first-page":"48","article-title":"ARIMA and regression in analytical review: an empirical test","volume":"53","author":"WR Kinney","year":"1978","journal-title":"Account Rev"},{"key":"pone.0322737.ref016","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/S0360-8352(98)00066-7","article-title":"The use of ARIMA models for reliability forecasting and analysis","volume":"35","author":"SL Ho","year":"1998","journal-title":"Comput Ind Eng"},{"key":"pone.0322737.ref017","doi-asserted-by":"crossref","first-page":"132306","DOI":"10.1016\/j.physd.2019.132306","article-title":"Fundamentals of recurrent neural network (RNN) and long short-term memory (LSTM) network","volume":"404","author":"A Sherstinsky","year":"2020","journal-title":"Phys D Nonlinear Phenom"},{"issue":"9","key":"pone.0322737.ref018","doi-asserted-by":"crossref","first-page":"1204","DOI":"10.1287\/mnsc.1040.0276","article-title":"Which GARCH model for option valuation?","volume":"50","author":"P Christoffersen","year":"2004","journal-title":"Manage Sci"},{"key":"pone.0322737.ref019","doi-asserted-by":"crossref","DOI":"10.1007\/978-981-13-2285-3_58","article-title":"Stock market price prediction using LSTM RNN","volume-title":"Emerging trends in expert applications and security","author":"K Pawar","year":"2019"},{"key":"pone.0322737.ref020","doi-asserted-by":"crossref","unstructured":"Sajal SZ, Jahan I, Nygard KE. A survey on cyber security threats and challenges in modern society. In: 2019 IEEE International Conference on Electro Information Technology (EIT). 2019, pp. 525\u20138. doi: 10.1109\/eit.2019.8833829","DOI":"10.1109\/EIT.2019.8833829"},{"key":"pone.0322737.ref021","doi-asserted-by":"crossref","first-page":"150199","DOI":"10.1109\/ACCESS.2020.3015966","article-title":"Predicting stock market trends using machine learning and deep learning algorithms via continuous and binary data; a comparative analysis","volume":"8","author":"M Nabipour","year":"2020","journal-title":"IEEE Access"},{"key":"pone.0322737.ref022","doi-asserted-by":"crossref","first-page":"101","DOI":"10.29007\/qgcz","article-title":"Stock price prediction using LSTM on Indian share market","volume":"63","author":"A Ghosh","year":"2019","journal-title":"EPiC Series Comput"},{"key":"pone.0322737.ref023","doi-asserted-by":"crossref","DOI":"10.1186\/s40537-021-00495-x","article-title":"Predicting LQ45 financial sector indices using RNN-LSTM","volume":"8","author":"S Hansun","year":"2021","journal-title":"J Big Data"},{"key":"pone.0322737.ref024","doi-asserted-by":"crossref","unstructured":"Samarawickrama AJP, Fernando TGI. A recurrent neural network approach in predicting daily stock prices an application to the Sri Lankan stock market. In: 2017 IEEE International Conference on Industrial and Information Systems (ICIIS). 2017:1\u20136. doi: 10.1109\/iciinfs.2017.8300345","DOI":"10.1109\/ICIINFS.2017.8300345"},{"issue":"6","key":"pone.0322737.ref025","doi-asserted-by":"crossref","first-page":"3234","DOI":"10.1016\/j.eswa.2014.12.003","article-title":"Recurrent neural network and a hybrid model for prediction of stock returns","volume":"42","author":"AM Rather","year":"2015","journal-title":"Expert Syst Appl"},{"key":"pone.0322737.ref026","unstructured":"Shui-Ling YU, Li Z. Stock price prediction based on ARIMA-RNN combined model. In: 4th International Conference on Social Science (ICSS 2017). 2017, pp. 1\u20136. DOI:1010.12783\/dtssehs\/icss2017\/19384"},{"key":"pone.0322737.ref027","doi-asserted-by":"crossref","unstructured":"Li C, Song D, Tao D. Multi-task recurrent neural networks and higher-order Markov random fields for stock price movement prediction. In: Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. 2019, pp. 1141\u201351. doi: 10.1145\/3292500.3330983","DOI":"10.1145\/3292500.3330983"},{"key":"pone.0322737.ref028","doi-asserted-by":"crossref","first-page":"71326","DOI":"10.1109\/ACCESS.2020.2985763","article-title":"Fractional neuro-sequential ARFIMA-LSTM for financial market forecasting","volume":"8","author":"AH Bukhari","year":"2020","journal-title":"IEEE Access"},{"key":"pone.0322737.ref029","doi-asserted-by":"crossref","first-page":"101421","DOI":"10.1016\/j.najef.2021.101421","article-title":"Forecasting stock index price using the CEEMDAN-LSTM model","volume":"57","author":"Y Lin","year":"2021","journal-title":"N Am J Econ Finance"},{"key":"pone.0322737.ref030","doi-asserted-by":"crossref","first-page":"117736","DOI":"10.1016\/j.eswa.2022.117736","article-title":"Forecasting the realized volatility of stock price index: a hybrid model integrating CEEMDAN and LSTM","volume":"206","author":"Y Lin","year":"2022","journal-title":"Expert Syst Appl"},{"key":"pone.0322737.ref031","doi-asserted-by":"crossref","unstructured":"Raza MR, Hussain W, Merigo JM. Cloud sentiment accuracy comparison using RNN, LSTM and GRU. In: 2021 Innovations in Intelligent Systems and Applications Conference (ASYU). 2021, pp. 1\u20135. doi: 10.1109\/asyu52992.2021.9599044","DOI":"10.1109\/ASYU52992.2021.9599044"},{"issue":"11","key":"pone.0322737.ref032","doi-asserted-by":"crossref","first-page":"14365","DOI":"10.1007\/s10639-023-12394-0","article-title":"A novel methodology using RNNLSTMML for predicting student\u2019s academic performance","volume":"29","author":"A Kukkar","year":"2024","journal-title":"Educ Inf Technol"},{"key":"pone.0322737.ref033","doi-asserted-by":"crossref","unstructured":"Nawej CM, Owolawi PA, Walingo T. Toward a realistic comparative analysis of recurrent neural network\u2019s methods via long-term memory approaches. In: International Congress on Information and Communication Technology. 2024, pp. 245-\u201362. doi: 10.1007\/978-981-97-5035-1_19","DOI":"10.1007\/978-981-97-5035-1_19"},{"issue":"1","key":"pone.0322737.ref034","doi-asserted-by":"crossref","first-page":"2309","DOI":"10.30574\/wjarr.2024.23.1.2156","article-title":"Enhancing stock market prediction accuracy with recurrent deep learning models: a case study on the CAC40 index","volume":"23","author":"A Tashakkori","year":"2024","journal-title":"World J Adv Res Rev"},{"issue":"4","key":"pone.0322737.ref035","doi-asserted-by":"crossref","first-page":"2277","DOI":"10.1007\/s10994-023-06471-1","article-title":"Forecasting of mobile network traffic and spatio\u2013temporal analysis using modLSTM","volume":"113","author":"VJ Aski","year":"2023","journal-title":"Mach Learn"},{"issue":"3","key":"pone.0322737.ref036","doi-asserted-by":"crossref","first-page":"1429","DOI":"10.3390\/app13031429","article-title":"Prediction of complex stock market data using an improved hybrid EMD-LSTM model","volume":"13","author":"M Ali","year":"2023","journal-title":"Appl Sci"},{"issue":"7","key":"pone.0322737.ref037","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pone.0199582","article-title":"Improving forecasting accuracy for stock market data using EMD-HW bagging","volume":"13","author":"AM Awajan","year":"2018","journal-title":"PLoS One"},{"key":"pone.0322737.ref038","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2020\/6431712","article-title":"A hybrid prediction method for stock price using LSTM and ensemble EMD","volume":"2020","author":"Y Yujun","year":"2020","journal-title":"Complexity"},{"issue":"8","key":"pone.0322737.ref039","doi-asserted-by":"crossref","DOI":"10.1016\/j.heliyon.2023.e18819","article-title":"Assessment of hybrid machine learning algorithms using TRMM rainfall data for daily inflow forecasting in Tr\u00eas Marias Reservoir, eastern Brazil","volume":"9","author":"E Gomaa","year":"2023","journal-title":"Heliyon"},{"issue":"12","key":"pone.0322737.ref040","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1049\/icp.2024.3412","article-title":"Structural vibration analysis and modal analysis based on EEMD","volume":"2024","author":"Q Zhang","year":"2025","journal-title":"IET Conf Proc"},{"issue":"6","key":"pone.0322737.ref041","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1049\/rpg2.12943","article-title":"Short-term power forecasting method for 5G photovoltaic base stations on non\u2010sunny days based on SDN-integrated INGO-BP and RGAN","volume":"18","author":"J Huang","year":"2024","journal-title":"IET Renewable Power Gen"},{"issue":"5","key":"pone.0322737.ref042","doi-asserted-by":"crossref","first-page":"1136","DOI":"10.3390\/rs14051136","article-title":"Kernel ridge regression hybrid method for wheat yield prediction with satellite-derived predictors","volume":"14","author":"AAM Ahmed","year":"2022","journal-title":"Remote Sensing"},{"key":"pone.0322737.ref043","doi-asserted-by":"crossref","unstructured":"Fang Y, Dumlao M, Aviles J. Research on monthly precipitation prediction model based on WOA-CEEMDAN-BiLSTM. In: 2024 6th International Conference on Internet of Things, Automation and Artificial Intelligence (IoTAAI). 2024, pp. 42\u20135. doi: 10.1109\/iotaai62601.2024.10692875","DOI":"10.1109\/IoTAAI62601.2024.10692875"},{"key":"pone.0322737.ref044","doi-asserted-by":"crossref","first-page":"107132","DOI":"10.1016\/j.knosys.2021.107132","article-title":"Unified deep learning approach for efficient intrusion detection system using integrated spatial-temporal features","volume":"226","author":"P Rajesh Kanna","year":"2021","journal-title":"Knowl-Based Syst"},{"issue":"4","key":"pone.0322737.ref045","doi-asserted-by":"crossref","first-page":"2407","DOI":"10.1007\/s11277-024-11607-0","article-title":"An enhanced hybrid intrusion detection using MapReduce-optimized black widow convolutional LSTM neural networks","volume":"138","author":"PR Kanna","year":"2024","journal-title":"Wireless Pers Commun"},{"issue":"2","key":"pone.0322737.ref046","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1007\/s12065-019-00295-6","article-title":"Development and performance evaluation of hybrid KELM models for forecasting of agro-commodity price","volume":"14","author":"N Parida","year":"2019","journal-title":"Evol Intel"},{"issue":"10","key":"pone.0322737.ref047","doi-asserted-by":"crossref","first-page":"2281","DOI":"10.1080\/15435075.2023.2301399","article-title":"Short-term wind speed forecasts through hybrid model based on improved variational mode decomposition","volume":"21","author":"D Yiyan","year":"2024","journal-title":"Int J Green Energy"},{"key":"pone.0322737.ref048","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.renene.2022.02.108","article-title":"A short-term wind power prediction model based on CEEMD and WOA-KELM","volume":"189","author":"Y Ding","year":"2022","journal-title":"Renew Energy"},{"key":"pone.0322737.ref049","doi-asserted-by":"crossref","unstructured":"Xiao H, Lin D, Chen S, Li S. Theoretical method and data validation of time series residual analysis based on iterative RNN model. 2023. doi: 10.2139\/ssrn.4586333","DOI":"10.2139\/ssrn.4586333"},{"key":"pone.0322737.ref050","doi-asserted-by":"crossref","first-page":"114543","DOI":"10.1016\/j.chaos.2024.114543","article-title":"Fractal properties, information theory, and market efficiency","volume":"180","author":"X Brouty","year":"2024","journal-title":"Chaos Soliton Fract"},{"issue":"18","key":"pone.0322737.ref051","doi-asserted-by":"crossref","first-page":"4630","DOI":"10.1016\/j.physa.2008.03.035","article-title":"Hurst exponent and prediction based on weak-form efficient market hypothesis of stock markets","volume":"387","author":"C Eom","year":"2008","journal-title":"Phys A Stat Mech Appl"},{"issue":"2","key":"pone.0322737.ref052","doi-asserted-by":"crossref","DOI":"10.1190\/1.2437700","article-title":"Application of the empirical mode decomposition and Hilbert-Huang transform to seismic reflection data","volume":"72","author":"BM Battista","year":"2007","journal-title":"Geophysics"},{"issue":"4","key":"pone.0322737.ref053","doi-asserted-by":"crossref","first-page":"163","DOI":"10.2113\/JEEG14.4.163","article-title":"Empirical mode decomposition operator for dewowing GPR data","volume":"14","author":"BM Battista","year":"2009","journal-title":"J Environ Eng Geophys"}],"container-title":["PLOS One"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0322737","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,2]],"date-time":"2025-06-02T13:28:19Z","timestamp":1748870899000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0322737"}},"subtitle":[],"editor":[{"given":"Jinran","family":"Wu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2025,6,2]]},"references-count":53,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,6,2]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pone.0322737","relation":{},"ISSN":["1932-6203"],"issn-type":[{"value":"1932-6203","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,2]]}}}