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Guerrero-Estrada AY, Quezada LF, Sun GH. Benchmarking quantum versions of the kNN algorithm with a metric based on amplitude-encoded features. Sci Rep 2024; 14:16697. [PMID: 39030254 PMCID: PMC11271630 DOI: 10.1038/s41598-024-67392-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2024] [Accepted: 07/10/2024] [Indexed: 07/21/2024] Open
Abstract
This work introduces a quantum subroutine for computing the distance between two patterns and integrates it into two quantum versions of the kNN classifier algorithm: one proposed by Schuld et al. and the other proposed by Quezada et al. Notably, our proposed subroutine is tailored to be memory-efficient, requiring fewer qubits for data encoding, while maintaining the overall complexity for both QkNN versions. This research focuses on comparing the performance of the two quantum kNN algorithms using the original Hamming distance with qubit-encoded features and our proposed subroutine, which computes the distance using amplitude-encoded features. Results obtained from analyzing thirteen different datasets (Iris, Seeds, Raisin, Mine, Cryotherapy, Data Bank Authentication, Caesarian, Wine, Haberman, Transfusion, Immunotherapy, Balance Scale, and Glass) show that both algorithms benefit from the proposed subroutine, achieving at least a 50% reduction in the number of required qubits, while maintaining a similar overall performance. For Shuld's algorithm, the performance improved in Cryotherapy (68.89% accuracy compared to 64.44%) and Balance Scale (85.33% F1 score compared to 78.89%), was worse in Iris (86.0% accuracy compared to 95.33%) and Raisin (77.67% accuracy compared to 81.56%), and remained similar in the remaining nine datasets. While for Quezada's algorithm, the performance improved in Caesarian (68.89% F1 score compared to 58.22%), Haberman (69.94% F1 score compared to 62.31%) and Immunotherapy (76.88% F1 score compared to 69.67%), was worse in Iris (82.67% accuracy compared to 95.33%), Balance Scale (77.97% F1 score compared to 69.21%) and Glass (40.04% F1 score compared to 28.79%), and remained similar in the remaining seven datasets.
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Affiliation(s)
| | - L F Quezada
- Research Center for Quantum Physics, Huzhou University, Huzhou, 313000, People's Republic of China.
| | - Guo-Hua Sun
- Computing Research Center, National Polytechnic Institute, 07700, Mexico City, Mexico
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2
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Wang J, Chen Z. Factor-GAN: Enhancing stock price prediction and factor investment with Generative Adversarial Networks. PLoS One 2024; 19:e0306094. [PMID: 38917175 PMCID: PMC11198854 DOI: 10.1371/journal.pone.0306094] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2023] [Accepted: 06/11/2024] [Indexed: 06/27/2024] Open
Abstract
Deep learning, a pivotal branch of artificial intelligence, has increasingly influenced the financial domain with its advanced data processing capabilities. This paper introduces Factor-GAN, an innovative framework that utilizes Generative Adversarial Networks (GAN) technology for factor investing. Leveraging a comprehensive factor database comprising 70 firm characteristics, Factor-GAN integrates deep learning techniques with the multi-factor pricing model, thereby elevating the precision and stability of investment strategies. To explain the economic mechanisms underlying deep learning, we conduct a subsample analysis of the Chinese stock market. The findings reveal that the deep learning-based pricing model significantly enhances return prediction accuracy and factor investment performance in comparison to linear models. Particularly noteworthy is the superior performance of the long-short portfolio under Factor-GAN, demonstrating an annualized return of 23.52% with a Sharpe ratio of 1.29. During the transition from state-owned enterprises (SOEs) to non-SOEs, our study discerns shifts in factor importance, with liquidity and volatility gaining significance while fundamental indicators diminish. Additionally, A-share listed companies display a heightened emphasis on momentum and growth indicators relative to their dual-listed counterparts. This research holds profound implications for the expansion of explainable artificial intelligence research and the exploration of financial technology applications.
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Affiliation(s)
- Jiawei Wang
- School of Finance, Shanghai University of Finance and Economics, Shanghai, China
| | - Zhen Chen
- School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China
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3
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Xie C, Wen X, Pang H, Zhang B. Application of graph auto-encoders based on regularization in recommendation algorithms. PeerJ Comput Sci 2023; 9:e1335. [PMID: 37346640 PMCID: PMC10280488 DOI: 10.7717/peerj-cs.1335] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2023] [Accepted: 03/17/2023] [Indexed: 06/23/2023]
Abstract
Social networking has become a hot topic, in which recommendation algorithms are the most important. Recently, the combination of deep learning and recommendation algorithms has attracted considerable attention. The integration of autoencoders and graph convolutional neural networks, while providing an effective solution to the shortcomings of traditional algorithms, fails to take into account user preferences and risks over-smoothing as the number of encoder layers increases. Therefore, we introduce L1 and L2 regularization techniques and fuse them linearly to address user preferences and over-smoothing. In addition, the presence of a large amount of noisy data in the graph data has an impact on feature extraction. To our best knowledge, most existing models do not account for noise and address the problem of noisy data in graph data. Thus, we introduce the idea of denoising autoencoders into graph autoencoders, which can effectively address the noise problem. We demonstrate the capability of the proposed model on four widely used datasets and experimentally demonstrate that our model is more competitive by improving up to 1.3, 1.4, and 1.2, respectively, on the edge prediction task.
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Affiliation(s)
- Chengxin Xie
- College of Information Engineering, Hebei University of Architecture, Zhangjiakou, China
| | - Xiumei Wen
- College of Information Engineering, Hebei University of Architecture, Zhangjiakou, China
- Big Data Technology Innovation Center of Zhangjiakou, Zhangjiakou, China
| | - Hui Pang
- College of Information Engineering, Hebei University of Architecture, Zhangjiakou, China
| | - Bo Zhang
- College of Information Engineering, Hebei University of Architecture, Zhangjiakou, China
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4
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Guevara E, Torres-Galván JC, González FJ, Luévano-Contreras C, Castillo-Martínez CC, Ramírez-Elías MG. Response to Comment on "Feasibility of Raman spectroscopy as a potential in vivo tool to screen for pre-diabetes and diabetes". JOURNAL OF BIOPHOTONICS 2023; 16:e202200322. [PMID: 36305890 DOI: 10.1002/jbio.202200322] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2022] [Accepted: 10/26/2022] [Indexed: 06/16/2023]
Abstract
This letter aims to reply to Bratchenko and Bratchenko's comment on our paper "Feasibility of Raman spectroscopy as a potential in vivo tool to screen for pre-diabetes and diabetes." Our paper analyzed the feasibility of using in vivo Raman measurements combined with machine learning techniques to screen diabetic and prediabetic patients. We argued that this approach yields high overall accuracy (94.3%) while retaining a good capacity to distinguish between diabetic (area under the receiver-operating curve [AUC] = 0.86) and control classes (AUC = 0.97) and a moderate performance for the prediabetic class (AUC = 0.76). Bratchenko and Bratchenko's comment focuses on the possible overestimation of the proposed classification models and the absence of information on the age of participants. In this reply, we address their main concerns regarding our previous manuscript.
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Affiliation(s)
- Edgar Guevara
- CONACYT-Universidad Autónoma de San Luis Potosí, San Luis Potosí, Mexico
| | - Juan Carlos Torres-Galván
- Terahertz Science and Technology Center (C2T2) and Science and Technology National Lab (LANCyTT), Universidad Autónoma de San Luis Potosí, San Luis Potosí, Mexico
- Facultad de Ingeniería, Universidad Autónoma de San Luis Potosí, San Luis Potosí, Mexico
| | - Francisco Javier González
- Terahertz Science and Technology Center (C2T2) and Science and Technology National Lab (LANCyTT), Universidad Autónoma de San Luis Potosí, San Luis Potosí, Mexico
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5
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Sun S, Wang R, An B. Reinforcement Learning for Quantitative Trading. ACM T INTEL SYST TEC 2023. [DOI: 10.1145/3582560] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
Quantitative trading (QT), which refers to the usage of mathematical models and data-driven techniques in analyzing the financial market, has been a popular topic in both academia and financial industry since 1970s. In the last decade, reinforcement learning (RL) has garnered significant interest in many domains such as robotics and video games, owing to its outstanding ability on solving complex sequential decision making problems. RL’s impact is pervasive, recently demonstrating its ability to conquer many challenging QT tasks. It is a flourishing research direction to explore RL techniques’ potential on QT tasks. This paper aims at providing a comprehensive survey of research efforts on RL-based methods for QT tasks. More concretely, we devise a taxonomy of RL-based QT models, along with a comprehensive summary of the state of the art. Finally, we discuss current challenges and propose future research directions in this exciting field.
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Affiliation(s)
- Shuo Sun
- Nanyang Technological University, Singapore
| | | | - Bo An
- Nanyang Technological University, Singapore
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6
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Riabykh A, Surzhko D, Konovalikhin M, Koltcov S. STTM: an efficient approach to estimating news impact on stock movement direction. PeerJ Comput Sci 2022; 8:e1156. [PMID: 37346316 PMCID: PMC10280229 DOI: 10.7717/peerj-cs.1156] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2022] [Accepted: 10/24/2022] [Indexed: 06/23/2023]
Abstract
Open text data, such as financial news, are thought to be able to affect or to describe stock market behavior, however, there are no widely accepted algorithms for extracting the relationship between stock quotes time series and fast-growing textual representation of economic information. The field remains challenging and understudied. In particular, topic modeling as a powerful tool for interpretable dimensionality reduction has been hardly ever used for such tasks. We present a topic modeling framework for assessing the relationship between financial news stream and stock prices in order to maximize trader's gain. To do so, we use a dataset of economic news sections of three Russian national media sources (Kommersant, Vedomosti, and RIA Novosti) containing 197,678 economic articles. They are used to predict 39 time series of the most liquid Russian stocks collected over eight years, from 2013 to 2021. Our approach shows the ability to detect significant return-predictive signals and outperforms 26 existing models in terms of Sharpe ratio and annual return of simple long strategy. In particular, it shows a significant Granger causal relationship for more than 70% of portfolio stocks. Furthermore, the approach produces highly interpretable results, requires no domain-specific dictionaries, and, unlike most existing industrial solutions, can be calibrated for individual time series. This makes it directly usable for trading strategies and analytical tasks. Finally, since topic modeling shows its efficiency for most European languages, our approach is expected to be transferrable to European stock markets as well.
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Affiliation(s)
- Aleksei Riabykh
- Department of Data Analysis and Modeling, VTB Bank, Moscow, Russia
| | - Denis Surzhko
- Department of Data Analysis and Modeling, VTB Bank, Moscow, Russia
| | | | - Sergei Koltcov
- Laboratory for Social and Cognitive Informatics, National Research University Higher School of Economics, St. Petersburg, Russia
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7
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Stock Trading Strategy of Reinforcement Learning Driven by Turning Point Classification. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-11019-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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8
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Automatic Detection of Sand Fouling Levels in Railway Tracks Using Supervised Machine Learning: A Case Study from Saudi Arabian Railway. ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2022. [DOI: 10.1007/s13369-022-07243-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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9
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Zeng X, Cai J, Liang C, Yuan C. A hybrid model integrating long short-term memory with adaptive genetic algorithm based on individual ranking for stock index prediction. PLoS One 2022; 17:e0272637. [PMID: 35976906 PMCID: PMC9385067 DOI: 10.1371/journal.pone.0272637] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2022] [Accepted: 07/25/2022] [Indexed: 11/30/2022] Open
Abstract
Modeling and forecasting stock prices have been important financial research topics in academia. This study seeks to determine whether improvements can be achieved by forecasting a stock index using a hybrid model and incorporating financial variables. We extend the literature on stock market forecasting by applying a hybrid model that combines wavelet transform (WT), long short-term memory (LSTM), and an adaptive genetic algorithm (AGA) based on individual ranking to predict stock indices for the Dow Jones Industrial Average (DJIA) index of the New York Stock Exchange, Standard & Poor's 500 (S&P 500) index, Nikkei 225 index of Tokyo, Hang Seng Index of Hong Kong market, CSI300 index of Chinese mainland stock market, and NIFTY50 index of India. The results indicate an overall improvement in forecasting of the stock index using the AGA-LSTM model compared to the benchmark models. The evaluation indicators prove that this model has a higher prediction accuracy when forecasting six stock indices.
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Affiliation(s)
- Xiaohua Zeng
- School of Economics and Trade, Guangzhou Xinhua University, Dongguan, China
| | - Jieping Cai
- School of Economics and Trade, Guangzhou Xinhua University, Dongguan, China
| | - Changzhou Liang
- School of Economics and Trade, Guangzhou Xinhua University, Dongguan, China
| | - Chiping Yuan
- Lingnan College, Sun Yat-Sen University, Guangzhou, China
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10
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Prediction of Self-Healing of Engineered Cementitious Composite Using Machine Learning Approaches. APPLIED SCIENCES-BASEL 2022. [DOI: 10.3390/app12073605] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
Engineered cementitious composite (ECC) is a unique material, which can significantly contribute to self-healing based on ongoing hydration. However, it is difficult to model and predict the self-healing performance of ECC. Although different machine learning (ML) algorithms have been utilized to predict several properties of concrete, the application of ML on self-healing prediction is considerably rare. This paper aims to provide a comparative analysis on the performance of various machine learning models in predicting the self-healing capability of ECC. These models include four individual methods, linear regression (LR), back-propagation neural network (BPNN), classification and regression tree (CART), and support vector regression (SVR). To improve prediction accuracy, three ensemble methods, namely bagging, AdaBoost, and stacking, were also studied. A series of experimental works on the self-healing performance of ECC samples was conducted, and the results were used to develop and compare the accuracy among the ML models. The comparison results showed that the Stack_LR model had the best predictive performance, showing the highest coefficient of determination (R2), the lowest root-mean-squared error (RMSE), and the smallest prediction error (MAE). Among all individual models studies, the BPNN model performed the best in terms of the RMSE and R2, while SVR performed the best in terms of the MAE. Furthermore, SVR had the smallest prediction error (MAE) for crack widths less than 60 μm or greater than 100 μm, while CART had the smallest prediction error (MAE) for crack widths between 60 μm and 100 μm. The study concluded that the individual and ensemble methods can be used to predict the self-healing of ECC. Ensemble models were able to improve the accuracy of prediction compared to the individual model used as their base learner, i.e., a 2.3% to 4.9% reduction in MAE. However, selecting an appropriate individual and ensemble method is critical. To improve the performance accuracy, researchers should employ different ensemble methods to compare their effectiveness with different ML models.
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11
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Bellocca GP, Attanasio G, Cagliero L, Fior J. Leveraging the momentum effect in machine learning-based cryptocurrency trading. MACHINE LEARNING WITH APPLICATIONS 2022. [DOI: 10.1016/j.mlwa.2022.100310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
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12
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Banner M, Alosert H, Spencer C, Cheeks M, Farid SS, Thomas M, Goldrick S. A decade in review: use of data analytics within the biopharmaceutical sector. Curr Opin Chem Eng 2021; 34:None. [PMID: 34926134 PMCID: PMC8665905 DOI: 10.1016/j.coche.2021.100758] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
There are large amounts of data generated within the biopharmaceutical sector. Traditionally, data analysis methods labelled as multivariate data analysis have been the standard statistical technique applied to interrogate these complex data sets. However, more recently there has been a surge in the utilisation of a broader set of machine learning algorithms to further exploit these data. In this article, the adoption of data analysis techniques within the biopharmaceutical sector is evaluated through a review of journal articles and patents published within the last ten years. The papers objectives are to identify the most dominant algorithms applied across different applications areas within the biopharmaceutical sector and to explore whether there is a trend between the size of the data set and the algorithm adopted.
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Affiliation(s)
- Matthew Banner
- Department of Biochemical Engineering, University College London, Gower Street, London WC1E 6BT, UK
| | - Haneen Alosert
- Department of Biochemical Engineering, University College London, Gower Street, London WC1E 6BT, UK
| | - Christopher Spencer
- Cell Culture Fermentation Sciences, Biopharmaceutical Development, BioPharmaceuticals R&D, AstraZeneca, Cambridge, UK
| | - Matthew Cheeks
- Cell Culture Fermentation Sciences, Biopharmaceutical Development, BioPharmaceuticals R&D, AstraZeneca, Cambridge, UK
| | - Suzanne S Farid
- Department of Biochemical Engineering, University College London, Gower Street, London WC1E 6BT, UK
| | - Michael Thomas
- Department of Biochemical Engineering, University College London, Gower Street, London WC1E 6BT, UK
- London Centre for Nanotechnology, University College London, Gordon Street, London WC1H 0AH, UK
| | - Stephen Goldrick
- Department of Biochemical Engineering, University College London, Gower Street, London WC1E 6BT, UK
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The Predictive Ability of Quarterly Financial Statements. INTERNATIONAL JOURNAL OF FINANCIAL STUDIES 2021. [DOI: 10.3390/ijfs9030050] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
A fundamental role of financial reporting is to provide information useful in forecasting future cash flows. Applying up-to-date time series modelling techniques, this study provides direct evidence on the usefulness of quarterly data in predicting future operating cash flows. Moreover, we show that the predictive gain from using quarterly data is larger for asset-heavy industries and industries with higher levels of earnings smoothness. This study contributes to the accounting literature by examining the usefulness of quarterly financial statements in predicting the realization of future cash flows. Our results help fill the gap in knowledge on quarterly financial statements and provide new insights on why the frequency of financial reporting matters. In addition, our findings have important policy implications for the ongoing debate over interim reporting requirements in multiple jurisdictions around the world.
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15
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Abstract
Legaltech refers to the application of new technologies to the world of law, to carry out tasks that, until recently, were performed by lawyers or other personnel working in law firms. From 2015 onwards the Lawtech alternative has emerged. In this work, the concepts of Legaltech and Lawtech have been analyzed by searching the two main scientific information databases such as Scopus and Wed of Science (WoS). There has been a clear trend to use the concept of Legaltech against Lawtech. Six clear research lines have been detected from the whole of the published documents regarding these concepts. These are the related to Computer Science, Justice, Legal profession, Legal design, Law firms, and Legal Education. It is proposed to use the term Legaltech to include all technological advances in the legal field. From the point of view of opportunities, the irruption of Legaltech will be able to offer accurate legal advice to the public, reducing the price of this and on the other hand, analyze large amounts of data that law firms and legal advisors will use to improve their management and increase their productivity. In short, Legaltech and Lawtech are opening up new opportunities in the legal sector encouraging technological innovation, giving greater access to legal services, even try to achieve the goal of universal access to justice.
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Thakkar A, Chaudhari K. Fusion in stock market prediction: A decade survey on the necessity, recent developments, and potential future directions. AN INTERNATIONAL JOURNAL ON INFORMATION FUSION 2021; 65:95-107. [PMID: 32868979 PMCID: PMC7448965 DOI: 10.1016/j.inffus.2020.08.019] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/10/2020] [Revised: 07/27/2020] [Accepted: 08/20/2020] [Indexed: 06/11/2023]
Abstract
Investment in a financial market is aimed at getting higher benefits; this complex market is influenced by a large number of events wherein the prediction of future market dynamics is challenging. The investors' etiquettes towards stock market may demand the need of studying various associated factors and extract the useful information for reliable forecasting. Fusion can be considered as an approach to integrate data or characteristics, in general, and enhance the prediction based on the combinational approach that can aid each other. We conduct a systematic approach to present a survey for the years 2011-2020 by considering articles that have used fusion techniques for various stock market applications and broadly categorize them into information fusion, feature fusion, and model fusion. The major applications of stock market include stock price and trend prediction, risk analysis and return forecasting, index prediction, as well as portfolio management. We also provide an infographic overview of fusion in stock market prediction and extend our survey for other finely addressed financial prediction problems. Based on our surveyed articles, we provide potential future directions and concluding remarks on the significance of applying fusion in stock market.
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Affiliation(s)
- Ankit Thakkar
- Department of Computer Science and Engineering, Institute of Technology, Nirma University, Ahmedabad 382 481, Gujarat, India
| | - Kinjal Chaudhari
- Department of Computer Science and Engineering, Institute of Technology, Nirma University, Ahmedabad 382 481, Gujarat, India
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Thakkar A, Chaudhari K. Predicting stock trend using an integrated term frequency–inverse document frequency-based feature weight matrix with neural networks. Appl Soft Comput 2020. [DOI: 10.1016/j.asoc.2020.106684] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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18
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Comparative Study on Exponentially Weighted Moving Average Approaches for the Self-Starting Forecasting. APPLIED SCIENCES-BASEL 2020. [DOI: 10.3390/app10207351] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Recently, a number of data analysists have suffered from an insufficiency of historical observations in many real situations. To address the insufficiency of historical observations, self-starting forecasting process can be used. A self-starting forecasting process continuously updates the base models as new observations are newly recorded, and it helps to cope with inaccurate prediction caused by the insufficiency of historical observations. This study compared the properties of several exponentially weighted moving average methods as base models for the self-starting forecasting process. Exponentially weighted moving average methods are the most widely used forecasting techniques because of their superior performance as well as computational efficiency. In this study, we compared the performance of a self-starting forecasting process using different existing exponentially weighted moving average methods under various simulation scenarios and real case datasets. Through this study, we can provide the guideline for determining which exponentially weighted moving average method works best for the self-starting forecasting process.
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