[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-569649-105":53,"doc-detail-569649-en":126},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","journal-of-mathematics-and-modeling-in-finance-jmmf-vol-6-winter-spring-2026-ethereum-price-prediction-with-a-grutransformer-encoder-hybrid-model","Journal of Mathematics and Modeling in Finance (JMMF) - Vol. 6 - Winter & Spring 2026 - Ethereum Price Prediction with a GRU–Transformer Encoder Hybrid Model","","Predicting Ethereum’s price remains difficult because cryptocurrency markets show extreme volatility and nonlinear dynamics. This study presents a GRU–Transformer Encoder hybrid model designed to learn both short- and long-term temporal dependencies for improved forecasting. Daily data from 2017–2023 is used, drawing Ethereum open/high/low prices and trading volume from Yahoo Finance, while adding Bitcoin’s closing price plus OBV and ATR. Pearson and Spearman analyses verify feature interdependence.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":51,"@type":70,"position":76},"https://docshare.wps.com/template/general/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/journal-of-mathematics-and-modeling-in-finance-jmmf-vol-6-winter-spring-2026-ethereum-price-prediction-with-a-grutransformer-encoder-hybrid-model/569649/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/journal-of-mathematics-and-modeling-in-finance-jmmf-vol-6-winter-spring-2026-ethereum-price-prediction-with-a-grutransformer-encoder-hybrid-model/569649.png","ImageObject",442,249,{"name":88,"@type":89},"EvelynWrites","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-19","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":47},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What hybrid model is proposed for Ethereum price forecasting?","Question",{"text":108,"@type":109},"The paper proposes a hybrid model integrating a GRU with a Transformer Encoder to capture both short-term and long-term temporal dependencies.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"What data sources and features are used to train the model?",{"text":113,"@type":109},"It uses daily historical data from 2017 to 2023 from Yahoo Finance, including Ethereum open, high, low prices, and trading volume, plus Bitcoin’s closing price and technical indicators OBV and ATR.",{"name":115,"@type":106,"acceptedAnswer":116},"How does the proposed model compare with baseline architectures?",{"text":117,"@type":109},"Under identical conditions, the hybrid model outperforms standalone GRU, LSTM, CNN, Transformer Encoder, and CNN–GRU hybrids, achieving an MAE of 0.007199 (about $34.03).","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},569649,1792093686,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":50,"category_name":51,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":47,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":135,"language":136,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":61,"update_tm":140,"read_time":141},687212989558,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Journal of Mathematics and Modeling in Finance (JMMF) Vol. 6, No. 1, Winter & Spring 2026  \nResearch paper  \nEthereum Price Prediction with a GRU–Transformer Encoder Hybrid Model  \nYones Esmaeelzade Aghdam 1 , Hamid Mesgarani2 , Ali Heidarvand3  \n1 Department of Mathematics, Faculty of Statistics, Mathematics and Computer Science, Allameh Tabataba’i University, Tehran, Iran  \n[yesmaeelzade@atu.ac.ir](yesmaeelzade@atu.ac.ir)  \n2 Department of Mathematics, Shahid Rajaee Teacher Training University, Tehran, Iran [hmesgarani@sru.ac.ir](hmesgarani@sru.ac.ir)  \n3 Department of Mathematics, Shahid Rajaee Teacher Training University, Tehran, Iran [heidarvand.ali@gmail.com](heidarvand.ali@gmail.com)  \nAbstract:  \nPredicting the price of Ethereum remains a significant challenge due to the extreme volatility and nonlinear dynamics inherent in the cryptocurrency market.  \nThis study proposes a novel hybrid model that integrates a Gated Recurrent Unit (GRU) with a Transformer Encoder to effectively capture both short-term and long-term temporal dependencies for enhanced Ethereum price forecasting. The model was trained on daily historical data from 2017 to 2023 . The dataset, sourced from Yahoo Finance, includes Ethereums open, high, and low prices, along with its trading volume. Additionally, Bitcoins closing price and two technical indicators, On-Balance Volume (OBV) and Average True Range (ATR), were incorporated.  \nPearson and Spearman correlation analyses confirmed strong interdependencies among the selected features. The model underwent training for 90 epochs, utilizing the Mean Squared Error (MSE) as the loss function and the Adam optimizer. Under identical experimental conditions, the proposed hybrid model significantly outperformed several baseline architectures, including standalone GRU, Long Short-Term Memory (LSTM), Convolutional Neural Network (CNN), Transformer Encoder, and CNN–GRU hybrid models. Specifically, the model achieved a Mean Absolute Error (MAE) of 0.007199 (equivalent to $34.03), which is considerably lower than Ethereums average daily price fluctuation of $74 .73. These findings demonstrate that the GRU–Transformer Encoder hybrid model is highly effective in extracting intricate patterns from volatile financial time series. Consequently, it can serve as a practical and robust tool for market trend analysis and risk management.  \nKeywords: Ethereum price prediction; cryptocurrency volatility; gated recurrent unit; Transformer encoder; financial time series; machine learning.  \nClassification: 97M30; 35R11; 35R02; 92B20 .  \n1 Introduction  \nEthereum stands as the worlds second-largest cryptocurrency by market capitalization, trailing only Bitcoin. However, unlike Bitcoin, which primarily functions as a  \n1 Corresponding author  \nReceived: 12/08/2025 Accepted: 22/11/2025  \n[https://doi.org/10.22054/JMMF.2025.87542.1204](https://doi.org/10.22054/JMMF.2025.87542.1204)  \nstore of value, Ethereum offers a robust infrastructure for executing smart contractsand hosting decentralized applications. These unique capabilities have propelled Ethereums widespread adoption across diverse domains, including decentralized finance, blockchain-based gaming, and the non-fungible token market.  \nThe cryptocurrency market, and Ethereum in particular, is notoriously volatile. These significant price fluctuations are influenced by a multitude of factors, such as international economic and geopolitical news, shifting market sentiment, and network-specific changes like system upgrades. Consequently, accurate prediction of Ethereums price is of paramount importance, not only for individual traders but also for major corporations and exchanges seeking effective risk management strategies.  \nThe inherent volatility of Ethereums price often renders traditional statistical models, such as ARIMA and GARCH, inadequate for accurate forecasting. Consequently, deep learning models, particularly GRU and LSTM, have gained widespread application in this field. Neverthele","cbCaiowjhjMOc3Uu","https://ap.wps.com/l/cbCaiowjhjMOc3Uu","pdf",685391,23,"English","# Abstract\n# Keywords\n# 1 Introduction","[{\"question\":\"What hybrid model is proposed for Ethereum price forecasting?\",\"answer\":\"The paper proposes a hybrid model integrating a GRU with a Transformer Encoder to capture both short-term and long-term temporal dependencies.\"},{\"question\":\"What data sources and features are used to train the model?\",\"answer\":\"It uses daily historical data from 2017 to 2023 from Yahoo Finance, including Ethereum open, high, low prices, and trading volume, plus Bitcoin’s closing price and technical indicators OBV and ATR.\"},{\"question\":\"How does the proposed model compare with baseline architectures?\",\"answer\":\"Under identical conditions, the hybrid model outperforms standalone GRU, LSTM, CNN, Transformer Encoder, and CNN–GRU hybrids, achieving an MAE of 0.007199 (about $34.03).\"}]","Journal of Mathematics and Modeling in Finance (JMMF) - Vol. 6 - Winter & Spring 2026 - Ethereum Price Prediction with a GRU–Transformer Encoder Hybrid Model | PDF",1791876858,8]