A multi-factor dynamic time series measure for stock correlation analysis

Jinyu Fan; Guanyu Lu; Jun Ma

doi:10.1371/journal.pone.0336173

Peer Review History

Original SubmissionAugust 13, 2025
8 Sep 2025 Decision Letter - Najmul Hasan, Editor PONE-D-25-44140A Multi-Factor Dynamic Time Series Measure for Stock Correlation AnalysisPLOS ONE Dear Dr. Ma, Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process. Please submit your revised manuscript by Oct 23 2025 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file. 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If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice. [Note: HTML markup is below. Please do not edit.] Reviewers' comments: Reviewer's Responses to Questions Comments to the Author 1. Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1: Yes Reviewer #2: Yes ******** 2. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: Yes Reviewer #2: Yes ****** 3. Have the authors made all data underlying the findings in their manuscript fully available? The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified. Reviewer #1: Yes Reviewer #2: No ****** 4. Is the manuscript presented in an intelligible fashion and written in standard English? PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here. Reviewer #1: Yes Reviewer #2: Yes ****** 5. Review Comments to the Author Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters) Reviewer #1: The article is interesting and relevant. It presents new theoretical results on improving methods for measuring the similarity of time series. The practical result of the research is an increase in the accuracy of financial analysis. The main contribution of the article is the development of a new approach to stock correlation analysis based on the multifactorial dynamic temporal similarity measure (MFDTSM). The authors integrated XGBoost with SHAP to quantitatively assess the impact of multidimensional factors on stock market dynamics and to cluster stocks based on their similarity in influence. The proposed method allows for both the multidimensionality of factors and time lags (TLE) to be taken into account. The manuscript is technically sound, and the data presented support the conclusions. The proposed MFDTSM method is theoretically well-founded, as it combines XGBoost with SHAP for reliable factor analysis and incorporates a cumulative distance matrix with optimal alignment to capture time-delayed dynamics. The methodology is described in sufficient detail to ensure reproducibility. The conclusions obtained are consistent with the experimental data and highlight the advantages of MFDTSM. There are some comments on the article: 1) In the Introduction section, the authors provided extensive information on time series analysis methods such as TLE, PPC, LCSS and DTW to emphasise the innovativeness of their proposed Multi-Factor Dynamic Temporal Similarity Measure (MFDTSM) method. However, the Introduction Section lacks information on modern time series analysis methods using neural networks. 2) Through their research, the authors demonstrated the high efficiency of the MFDTSM method. However, they paid little attention to analysing how sensitive the results were to the choice of XGBoost hyperparameters and clustering parameters. 3) The authors provided little information on how they selected the 12 measurement factors. There is also no information on how the selection of factors affects the stability of the model. This information should be added to the Conclusions section. Reviewer #2: Stocks represent a meaningful investment avenue, and how to effectively analyze stock trends is a key focus and challenge for researchers. The authors propose a Multi-Factor Dynamic Temporal Similarity Measure (MFDTSM), which significantly improves the accuracy of analyzing industry correlation, linear correlation, and stock correlation pricing. This article has a reasonable structure, standard and accurate language, and provides sufficient explanations of principles and methods; its results also have strong guiding significance. However, the article has slight deficiencies in data description, such as specifying which 102 stocks are included, how many stocks belong to the communication industry and the financial industry respectively, what the 12 key stock factors are, and the specific analysis process. 1. It would be more intuitive if a list of the 102 stocks could be provided. 2. It is recommended to label the meanings of different types in Figure 3 to make it easier for readers to understand the content of the figure. ****** 6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy. Reviewer #1: No Reviewer #2: No ******** [NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.] While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step. https://doi.org/10.1371/journal.pone.0336173.r001
Revision 1
8 Oct 2025 Author Response Response to Reviewers Manuscript ID: PONE-D-25-44140 Title: A Multi-Factor Dynamic Time Series Measure for Stock Correlation Analysis Dear Dr. Najmul Hasan and Reviewers, We sincerely thank the editors and reviewers for their valuable time and insightful comments on our manuscript. These comments have significantly helped us improve the quality and clarity of our work. We have carefully addressed all the points raised. Below is our point-by-point response to the comments from Reviewer 1 and Reviewer 2. Changes in the manuscript have been highlighted in yellow in the revised manuscript file with track changes. Responses to Reviewer 1: Comment 1: In the Introduction section, the authors provided extensive information on time series analysis methods such as TLE, PPC, LCSS and DTW to emphasise the innovativeness of their proposed Multi-Factor Dynamic Temporal Similarity Measure (MFDTSM) method. However, the Introduction Section lacks information on modern time series analysis methods using neural networks. Response: We sincerely thank the reviewer for this excellent suggestion. We agree that discussing modern neural network-based approaches is crucial for positioning our work within the current research landscape. We have now added a new paragraph in the Introduction section that introduces prevalent deep learning methods like LSTM, GRU, and Transformers for time series analysis. The added text acknowledges their strengths in capturing complex temporal dependencies while also explaining our methodological choice by highlighting their limitations relative to the goals of our study, particularly regarding interpretability of factor-specific influences and explicit modeling of dynamic phase shifts in time-lag effects. This addition provides a more comprehensive background and better underscores the unique niche our MFDTSM method aims to fill. Action Taken: Added a new paragraph on modern neural network methods in the Introduction. And the newly added paragraph is as follows: In recent years, deep learning approaches, particularly neural network-based models such as Long Short-Term Memory (LSTM) , Gated Recurrent Units (GRU) , and Transformers , have also been widely adopted for time series analysis due to their ability to capture complex temporal dependencies and nonlinear patterns. For instance, LSTMs have been successfully applied in stock price prediction and portfolio optimization, while attention mechanisms enhance the model’s focus on salient time steps. However, these methods often require large amounts of data and computational resources, and their black-box nature can limit interpretability in factor-specific analysis. Although neural networks excel in pattern recognition, they are less focused on explicitly modeling factor influence and dynamic phase shifts in time-lag effects, which are central to our proposed MFDTSM framework. Comment 2: Through their research, the authors demonstrated the high efficiency of the MFDTSM method. However, they paid little attention to analysing how sensitive the results were to the choice of XGBoost hyperparameters and clustering parameters. Response: We thank the reviewer for raising this important point regarding the sensitivity and robustness of our model. To address this, we have expanded the Experimental Setup section with a more detailed explanation of our hyperparameter selection process. We now explicitly state that key hyperparameters, including the number of clusters (c=5) and the phase change rate coefficient (μ=1), were determined through a grid search and cross-validation process to ensure robustness. We also mention that we employed the Silhouette Score and Elbow Method to evaluate and confirm the optimal choice of the cluster number. Furthermore, we note that although the model performance is relatively stable across slight variations in these parameters, we recommend more advanced methods like Bayesian optimization for future work. This addition demonstrates our careful consideration of parameter tuning and enhances the reproducibility of our study. Action Taken: Enhanced the description of hyperparameter selection in the Experimental Setup section. And the newly added paragraph is as follows: The selection of hyperparameters, including the number of clusters c = 5 and the phase change rate coefficient μ = 1, was determined through a grid search and cross-validation process to ensure robustness. We evaluated clustering performance using the Silhouette Score and Elbow Method, which indicated that c = 5 optimally balances intra-cluster cohesion and inter-cluster separation. Similarly, μ was tuned in the range [0.5, 2.0] to minimize prediction error in a validation set. Although the model performance is relatively stable across slight variations in these parameters, future work could incorporate Bayesian optimization for more efficient hyperparameter tuning. Comment 3: The authors provided little information on how they selected the 12 measurement factors. There is also no information on how the selection of factors affects the stability of the model. This information should be added to the Conclusions section. Response: We appreciate the reviewer for this critical feedback. We have now added a comprehensive paragraph in the Conclusions section to address both parts of this comment. Firstly, we explain that the selection of the 12 factors (e.g., price, turnover rate, moving averages) was based on two criteria: (1) their established importance and consensus in existing financial literature, and (2) a preliminary feature importance analysis conducted using tree-based models. Secondly, and more importantly, we directly address the model's stability concerning factor selection. We describe that we conducted a sensitivity analysis by alternately excluding one factor at a time and observing the fluctuation in the model's similarity accuracy. The results showed that the model maintains robust performance with a minimal variation in accuracy (±2.3% in Mean Absolute Percentage Error, MAPE), indicating that MFDTSM is not overly reliant on any single factor and is generally stable under factor variations. This new analysis provides concrete evidence for the robustness of our method. Action Taken: Added a new paragraph detailing factor selection and stability analysis in the Conclusions section. And the newly added paragraph is as follows: Furthermore, the selection of the 12 stock factors (e.g., price, turnover rate, moving averages) was based on both the established financial research consensus and preliminary feature importance analysis using tree-based models. These factors are widely recognized as key indicators of stock performance and market behavior. To assess the stability of MFDTSM with respect to factor selection, we conducted sensitivity analyses by alternately excluding one factor at a time. The results showed that the model maintains robust performance with minimal fluctuation in similarity accuracy (±2.3% in Mean Absolute Percentage Error, MAPE), indicating that MFDTSM is not overly reliant on any single factor and is generally stable under factor variation. Once again, we express our deepest gratitude to the reviewers and editors for their constructive comments, which have greatly improved our manuscript. We look forward to the positive consideration of our revised paper. Responses to Reviewer 2: Comment 1: It would be more intuitive if a list of the 102 stocks could be provided. Response: We sincerely thank the reviewer for this valuable suggestion. To enhance the transparency and reproducibility of our study, we have now included a complete list of the 102 stocks used in our analysis as supplementary material. The list details the stock codes, stock names, primary industries (L1), and secondary industries (L2) based on the Shenwan Industry Classification Standard. Specifically, the dataset comprises 73 stocks from the Communication industry and 29 stocks from the Financial industry, covering diverse sub-sectors such as Communication Equipment, Communication Operations, Computer Applications, Bank, Real Estate, and others. This addition allows readers to better understand the dataset composition and facilitates further validation and replication of our study. Action Taken: We have added a supplementary file named “S1_Table.xlsx” containing the complete stock list. Stock Code,Stock Name,Industry (L1),Industry (L2) 000063,ZTE Corporation,Communication,Communication Equipment 000547,Aerospace Development,Communication,Communication Equipment 000561,Fenghuo Electronics,Communication,Communication Equipment 000586,Huiyuan Communication,Communication,Communication Equipment 000665,Hubei Broadcasting,Communication,Communication Operations 000701,Xiamen Xinda,Communication,Communication Operations 000725,BOE Technology Group,Communication,Optoelectronic Devices 000748,Great Wall Information,Communication,Computer Applications 000777,Zhonghe Technology,Communication,Communication Equipment 000839,CITIC Guoan,Communication,Communication Operations 000876,New Hope,Communication,Communication Operations 000938,Unisplendour Corporation,Communication,Computer Equipment 000988,Huagong Tech,Communication,Communication Equipment 002049,Unigroup Guoxin,Communication,Integrated Circuits 002089,Sunsea Telecommunications,Communication,Communication Equipment 002093,Guomai Technologies,Communication,Communication Operations 002104,Hengbao Co., Ltd.,Communication,Computer Applications 002115,Sunwave Communications,Communication,Communication Equipment 002151,BDStar Navigation,Communication,Communication Equipment 002161,Yuanwanggu,Communication,Communication Equipment 002194,Wuhan Fangu,Communication,Communication Equipment 002212,Topsec Technologies,Communication,Computer Applications 002231,Allwin Telecommunications,Communication,Communication Equipment 002261,TOWIN Information,Communication,Computer Applications 002281,Accelink Technologies,Communication,Communication Equipment 002296,Splendor Science & Technology,Communication,Computer Applications 002313,Sunsea IoT,Communication,Communication Equipment 002316,Yalian Development,Communication,Computer Applications 002396,Star-net Communication,Communication,Communication Equipment 002417,Shennan Circuits,Communication,Computer Applications 002465,Haige Communications,Communication,Communication Equipment 002467,263 Network,Communication,Communication Operations 002544,P&T Technology,Communication,Communication Equipment 300050,Dingli Communications,Communication,Communication Operations 300051,35 Internet,Communication,Computer Applications 300052,Zhongqingbao,Communication,Internet Services 300074,Huaping Stock,Communication,Computer Applications 300098,Gaoxin Development,Communication,Communication Equipment 300134,Taffull Technology,Communication,Communication Equipment 300136,Sunway Communication,Communication,Communication Equipment 300166,Beyondsoft,Communication,Computer Applications 300168,Wonders Information,Communication,Computer Applications 300177,Zhonghaida,Communication,Communication Equipment 300209,Tianze Information,Communication,Computer Applications 300226,Shanghai Steel Union,Communication,Internet Services 300245,Tianji Technology,Communication,Computer Applications 300250,Chuling Information,Communication,Communication Equipment 300252,Jinxinnuo,Communication,Communication Equipment 300264,Jachung Vision,Communication,Computer Applications 300288,Langma Information,Communication,Computer Applications 300290,Rongke Technology,Communication,Computer Applications 600050,China Unicom,Communication,Communication Operations 600105,Yongding Stock,Communication,Communication Equipment 600130,Bird Corporation,Communication,Communication Equipment 600198,Datang Telecom,Communication,Communication Equipment 600345,Changjiang Communication,Communication,Communication Equipment 600485,Xinwei Group,Communication,Communication Operations 600487,Hengtong Optic-Electric,Communication,Communication Equipment 600498,FiberHome Telecommunications,Communication,Communication Equipment 600522,Zhongtian Technology,Communication,Communication Equipment 600536,China National Software,Communication,Computer Applications 600570,Hundsun Technologies,Communication,Computer Applications 600588,Yonyou Network,Communication,Computer Applications 600637,Oriental Pearl,Communication,Communication Operations 600640,Guomai Culture,Communication,Communication Operations 600776,Eastern Communications,Communication,Communication Equipment 600797,Insigma Technology,Communication,Computer Applications 600804,Dr. Peng Telecom,Communication,Communication Operations 600845,Baosight Software,Communication,Computer Applications 600850,East China Computer,Communication,Computer Applications 600980,Beikang Technology,Communication,Communication Equipment 603000,People.cn,Communication,Internet Services 603160,Goodix Technology,Communication,Integrated Circuits 000001,Ping An Bank,Financial,Bank 000002,Vanke A,Financial,Real Estate 000006,Shenzhen Zhenye A,Financial,Real Estate 000012,CSG A,Financial,Real Estate 000046,Oceanwide Holdings,Financial,Real Estate 000069,OCT Group A,Financial,Real Estate 000402,Financial Street,Financial,Real Estate 000415,Bohai Leasing,Financial,Other Financial 000416,Minsheng Holdings,Financial,Other Financial 000417,Hefei Department Store,Financial,Other Financial 000419,Tongcheng Holdings,Financial,Other Financial 000420,Jilin Chemical Fiber,Financial,Other Financial 000421,Nanjing Public Utility,Financial,Other Financial 000423,Dong-E-E-Jiao,Financial,Other Financial 000425,XCMG Construction Machinery,Financial,Other Financial 000426,Xingye Mining,Financial,Other Financial 000428,Huatian Hotel,Financial,Other Financial 000429,Guangdong Expressway A,Financial,Other Financial 000430,Zhangjiajie Tourism,Financial,Other Financial 000488,Chenming Paper,Financial,Other Financial 000498,Shandong Road & Bridge,Financial,Other Financial 000501,Wushang Group A,Financial,Other Financial 000503,Guoxin Health,Financial,Other Financial 000506,Zhongrun Resources,Financial,Other Financial 000507,Zhuhai Port,Financial,Other Financial 000509,Huasu Holdings,Financial,Other Financial 000510,Xin Jinlu,Financial,Other Financial 000513,Livzon Group,Financial,Other Financial 000514,Yujian Development,Financial,Real Estate 000063,ZTE Corporation,Communication,Communication Equipment 000547,Aerospace Development,Communication,Communication Equipment 000561,Fenghuo Electronics,Communication,Communication Equipment 000586,Huiyuan Communication,Communication,Communication Equipment 000665,Hubei Broadcasting,Communication,Communication Operations 000701,Xiamen Xinda,Communication,Communication Operations 000725,BOE Technology Group,Communication,Optoelectronic Devices 000748,Great Wall Information,Communication,Computer Applications 000777,Zhonghe Technology,Communication,Communication Equipment 000839,CITIC Guoan,Communication,Communication Operations 000876,New Hope,Communication,Communication Operations 000938,Unisplendour Corporation,Communication,Computer Equipment 000988,Huagong Tech,Communication,Communication Equipment 002049,Unigroup Guoxin,Communication,Integrated Circuits 002089,Sunsea Telecommunications,Communication,Communication Equipment 002093,Guomai Technologies,Communication,Communication Operations 002104,Hengbao Co., Ltd.,Communication,Computer Applications 002115,Sunwave Communications,Communication,Communication Equipment 002151,BDStar Navigation,Communication,Communication Equipment 002161,Yuanwanggu,Communication,Communication Equipment Comment 2: It is recommended to label the meanings of different types in Figure 3 to make it easier for readers to understand the content of the figure. Response: We sincerely thank the reviewer for this valuable and constructive suggestion. We agree that clarifying the elements of Figure 3 is crucial for helping readers intuitively understand the distribution and comparison of prediction errors across different methods. In response to this comment, we have implemented the following comprehensive revisions to the figure and its corresponding des Attachments Attachment Submitted filename: Responses to Reviewer .docx https://doi.org/10.1371/journal.pone.0336173.r002
22 Oct 2025 Decision Letter - Najmul Hasan, Editor A Multi-Factor Dynamic Time Series Measure for Stock Correlation Analysis PONE-D-25-44140R1 Dear Dr. Ma, We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements. Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication. An invoice will be generated when your article is formally accepted. Please note, if your institution has a publishing partnership with PLOS and your article meets the relevant criteria, all or part of your publication costs will be covered. Please make sure your user information is up-to-date by logging into Editorial Manager at Editorial Manager® and clicking the ‘Update My Information' link at the top of the page. 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If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation. Reviewer #1: All comments have been addressed Reviewer #2: All comments have been addressed ******** 2. Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1: Yes Reviewer #2: Yes ****** 3. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: Yes Reviewer #2: Yes ****** 4. Have the authors made all data underlying the findings in their manuscript fully available? The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified. Reviewer #1: Yes Reviewer #2: Yes ****** 5. Is the manuscript presented in an intelligible fashion and written in standard English? PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here. Reviewer #1: Yes Reviewer #2: Yes ****** 6. Review Comments to the Author Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters) Reviewer #1: The authors have made significant efforts to address all of my previous comments. I am satisfied with the responses I have received to all of my remarks. They have added a new paragraph to the introduction discussing modern neural network methods. They have also improved the description of hyperparameter selection in the 'Experimental Setup' section. Furthermore, they have included a new paragraph in the 'Conclusions' section that provides a detailed explanation of factor selection and stability analysis. Overall, the authors have taken all of my comments into account. I am satisfied with the revised manuscript and consider it to be of high quality. Therefore, I recommend accepting the paper for publication. Reviewer #2: Thank you for the authors' careful response. Your explanations have basically addressed my questions. Personally, I believe the revised paper has a more rigorous logical structure, clearer thinking, and is easier for readers to understand. The revised article basically meets the journal's requirements, and I recommend accepting it for publication. ****** 7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy. Reviewer #1: Yes: Andrii Semenov Reviewer #2: Yes: Kaitao Li ******** https://doi.org/10.1371/journal.pone.0336173.r003
Formally Accepted
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