Paper: arXiv 2405.18938

Abstract

We introduce a novel large-scale deep learning model for Limit Order Book mid-price changes forecasting, and we name it `HLOB’. This architecture (i) exploits the information encoded by an Information Filtering Network, namely the Triangulated Maximally Filtered Graph, to unveil deeper and non-trivial dependency structures among volume levels; and (ii) guarantees deterministic design choices to handle the complexity of the underlying system by drawing inspiration from the groundbreaking class of Homological Convolutional Neural Networks. We test our model against 9 state-of-the-art deep learning alternatives on 3 real-world Limit Order Book datasets, each including 15 stocks traded on the NASDAQ exchange, and we systematically characterize the scenarios where HLOB outperforms state-of-the-art architectures. Our approach sheds new light on the spatial distribution of information in Limit Order Books and on its degradation over increasing prediction horizons, narrowing the gap between microstructural modeling and deep learning-based forecasting in high-frequency financial markets.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces advanced concepts like Homological Convolutional Neural Networks and Triangulated Maximally Filtered Graphs, indicating high mathematical density, while it rigorously tests the model against 9 alternatives on 3 real-world NASDAQ datasets with systematic characterization, demonstrating strong empirical implementation and backtest-readiness.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Mid-Price Change Forecasting"] --> B["Data Inputs<br>3 NASDAQ Limit Order Book Datasets"]
  B --> C["Proposed Methodology<br>HLOB Architecture"]
  C --> D["Component 1<br>Triangulated Maximally Filtered Graph<br>Information Filtering"]
  C --> E["Component 2<br>Homological Convolutional Neural Networks<br>Spatial Processing"]
  D & E --> F["Computational Process<br>Deep Learning Prediction"]
  F --> G["Key Findings & Outcomes<br>State-of-the-Art Performance &<br>Information Structure Insight"]

Cited References (342)

  1. NASDAQ Official Website
  2. What is LOBSTER?
  3. NASDAQ Stock Screener
  4. Quantitative portfolio management: The art and science of statistical arbitrage (2021)
  5. Companies Market Cap
  6. Deep reinforcement learning for active high frequency trading (2021) — link
  7. Trades, quotes and prices: financial markets under the microscope (2018)
  8. LOB-Based Deep Learning Models for Stock Price Trend Prediction: A Benchmark Study — → 2308.01915
and 334 more
  1. Towards Robust Representation of Limit Orders Books for Deep Learning Models (2021) — link
  2. The short-term predictability of returns in order book markets: a deep learning perspective (2022) — link
  3. A survey of data leakage detection and prevention solutions (2012)
  4. Transaction costs (1989)
  5. Market microstructure: A survey (2000)
  6. Market microstructure: A survey of microfoundations, empirical results, and policy implications (2005)
  7. Econophysics review: I. Empirical facts (2011)
  8. Econophysics review: II. Agent-based models (2011)
  9. Statistical modeling of high-frequency financial data (2011)
  10. Limit order books (2013)
  11. Limit order books (2016)
  12. Statistical properties of stock order books: empirical results and models (2002)
  13. Empirical analysis of limit order markets (2004)
  14. The price impact of order book events: market orders, limit orders and cancellations (2012)
  15. Order flow and price formation (2021) — link
  16. A continuous and efficient fundamental price on the discrete order book grid (2018)
  17. An empirical behavioral model of price formation (2005)
  18. The price impact of order book events (2014)
  19. High-frequency trading in a limit order book (2008)
  20. Enhancing trading strategies with order book signals (2018)
  21. Optimal execution with limit and market orders (2015)
  22. Limit order strategic placement with adverse selection risk and the role of latency (2017)
  23. Exogenous and endogenous price jumps belong to different dynamical classes (2022)
  24. Studies of the limit order book around large price changes (2009)
  25. Price jump prediction in limit order book (2012) — link
  26. Universal features of price formation in financial markets: perspectives from deep learning (2021)
  27. Daily volume forecasting using high frequency predictors (2010)
  28. Identifying expensive trades by monitoring the limit order book (2017)
  29. Effects of the limit order book on price dynamics (2014)
  30. Designating market maker behaviour in limit order book markets (2018)
  31. Stock market analysis: A review and taxonomy of prediction techniques (2019)
  32. Using deep learning to detect price change indications in financial markets (2017)
  33. Forecasting stock prices from the limit order book using convolutional neural networks (2017)
  34. Time-series classification using neural bag-of-features (2017)
  35. Machine learning for forecasting mid-price movements using limit order book data (2019)
  36. Using deep learning for price prediction by exploiting stationary limit order book features (2020)
  37. Improving Deep Learning of Alpha Term Structures from the Order Book (2024)
  38. Self-organised criticality in high frequency finance: the case of flash crashes (2021) — link
  39. Heterogeneous criticality in high frequency finance: a phase transition in flash crashes (2022)
  40. Temporal attention-augmented bilinear network for financial time-series data analysis (2018)
  41. Deep adaptive input normalization for time series forecasting (2019)
  42. Multi-head temporal attention-augmented bilinear network for financial time series prediction (2022)
  43. Augmented bilinear network for incremental multi-stock time-series classification (2023)
  44. Data normalization for bilinear structures in high-frequency financial time-series (2021)
  45. Transformers for limit order books (2020) — link
  46. Temporal logistic neural bag-of-features for financial time series forecasting leveraging limit order book data (2020)
  47. Introduction to the bag of features paradigm for image classification and retrieval (2011) — link
  48. Deep learning for market by order data (2021)
  49. Attention-based neural bag-of-features learning for sequence data (2022)
  50. Multi-horizon forecasting for limit order books: Novel deep learning approaches and hardware acceleration using intelligent processing units (2021) — link
  51. Forecasting the Mid-price Movements with High-Frequency LOB: A Dual-Stage Temporal Attention-Based Deep Learning Architecture (2023)
  52. Axial-LOB: High-Frequency Trading with Axial Attention (2022)
  53. Price dynamics in a Markovian limit order market (2013)
  54. Market microstructure design and flash crashes: A simulation approach (2013)
  55. Effects of limit order book information level on market stability metrics (2017)
  56. Market making with signals through deep reinforcement learning (2021)
  57. Deep reinforcement learning for market making (2020)
  58. Reinforcement learning approaches to optimal market making (2021)
  59. Deep Reinforcement Learning for High-Frequency Market Making (2023)
  60. JAX-LOB: A GPU-Accelerated limit order book simulator to unlock large scale reinforcement learning for trading (2023)
  61. Asynchronous Deep Double Duelling Q-Learning for Trading-Signal Execution in Limit Order Book Markets — → 2301.08688
  62. Reinforcement learning for optimized trade execution (2006)
  63. Machine learning for market microstructure and high frequency trading (2013)
  64. Modelling limit order trading with a continuous action policy for deep reinforcement learning (2023)
  65. Diversity-driven knowledge distillation for financial trading using deep reinforcement learning (2021)
  66. Deep reinforcement learning for financial trading using price trailing (2019)
  67. Benchmark dataset for mid-price forecasting of limit order book data with machine learning methods (2018)
  68. FinRL-Meta: Market environments and benchmarks for data-driven financial reinforcement learning (2022)
  69. Predicting stock price changes based on the limit order book: a survey (2022)
  70. Deep order flow imbalance: Extracting alpha at multiple horizons from the limit order book (2023)
  71. How and When are High-Frequency Stock Returns Predictable? (2022)
  72. Dependency structures in cryptocurrency market from high to low frequency (2022)
  73. Anatomy of a Stablecoin’s failure: The Terra-Luna case (2023)
  74. FTX’s downfall and Binance’s consolidation: the fragility of Centralized Digital Finance — → 2302.11371
  75. Gradient-based learning applied to document recognition (1998)
  76. An introduction to convolutional neural networks (2015) — link
  77. Understanding of a convolutional neural network (2017)
  78. Long short-term memory (1997)
  79. A review on the long short-term memory model (2020)
  80. Decoupled weight decay regularization (2017) — link
  81. Adam: A method for stochastic optimization (2014) — link
  82. nanoGPT
  83. Language models are few-shot learners (2020)
  84. UCL HPC CLuster Specs
  85. Pytorch: An imperative style, high-performance deep learning library (2019)
  86. Dark trading and price discovery (2015)
  87. An ecological perspective on the future of computer trading (2013)
  88. Are you playing in a toxic dark pool (2008)
  89. Shedding light on dark liquidity pools (2008)
  90. Institutional trading and alternative trading systems (2003)
  91. Deep learning (2015)
  92. Entropy optimized feature-based bag-of-words representation for information retrieval (2016)
  93. Multidimensional sequence classification based on fuzzy distances and discriminant analysis (2012)
  94. Optimal liquidation in dark pools (2014)
  95. How markets slowly digest changes in supply and demand (2009)
  96. How market ecology explains market malfunction (2021)
  97. The Impact of High Frequency Trading on the Canadian Market (2009)
  98. High-frequency trading, stock volatility, and price discovery (2010)
  99. The impact of high-frequency trading on markets (2011)
  100. A dysfunctional role of high frequency trading in electronic markets (2012)
  101. Where is the value in high frequency trading? (2012)
  102. Deep learning for limit order books (2019)
  103. Sequence classification of the limit order book using recurrent neural networks (2018)
  104. Mutual information between order book layers (2022)
  105. Elementary principles in statistical mechanics (1902)
  106. Activation functions: Comparison of trends in practice and research for deep learning (2018) — link
  107. Deep LOB trading: Half a second please! (2023)
  108. Trading with the momentum transformer: an intelligent and interpretable architecture (2021) — link
  109. Attention is all you need (2017)
  110. Deep unsupervised learning using nonequilibrium thermodynamics (2015)
  111. Denoising diffusion probabilistic models (2020)
  112. Generative modeling by estimating gradients of the data distribution (2019)
  113. Improved denoising diffusion probabilistic models (2021)
  114. Are transformers effective for time series forecasting? (2023)
  115. Informer: Beyond efficient transformer for long sequence time-series forecasting (2021)
  116. Transformers in time series: A survey (2022) — link
  117. Homological Convolutional Neural Networks (2023) — link
  118. Sparsification and Filtering for Spatial-temporal GNN in Multivariate Time-series (2022) — link
  119. Delving deep into rectifiers: Surpassing human-level performance on imagenet classification (2015)
  120. Recurrent convolutional neural networks for text classification (2015)
  121. Deep learning for audio signal processing (2019)
  122. Well-tuned simple nets excel on tabular datasets (2021)
  123. Trust issues: Uncertainty estimation does not enable reliable ood detection on medical tabular data (2020)
  124. Deep learning and the electrocardiogram: review of the current state-of-the-art (2021)
  125. Robust cognitive load detection from wrist-band sensors (2021)
  126. Deep learning: A primer for psychologists. (2021)
  127. An explainable AI decision-support-system to automate loan underwriting (2020)
  128. Explainable AI (XAI) models applied to the multi-agent environment of financial markets (2021)
  129. Sequential deep learning for credit risk monitoring with tabular financial data (2020) — link
  130. Blockchain for explainable and trustworthy artificial intelligence (2020)
  131. Deep learning based recommender system: A survey and new perspectives (2019)
  132. Neural time-aware sequential recommendation by jointly modeling preference dynamics and explicit feature couplings (2021)
  133. Recommendation system based on deep learning methods: a systematic review and new directions (2020)
  134. Why are deep learning models not consistently winning recommender systems competitions yet? A position paper (2020)
  135. A survey of data mining and machine learning methods for cyber security intrusion detection (2015)
  136. Cybersecurity in big data era: From securing big data to data-driven security (2019)
  137. Editorial deep learning for anomaly detection (2022)
  138. Multiview Deep Anomaly Detection: A Systematic Exploration (2022)
  139. Comparison of anomaly detectors: context matters (2021)
  140. Classification-based anomaly detection for general data (2020) — link
  141. Xgboost: A scalable tree boosting system (2016)
  142. Representation compression and generalization in deep neural networks (2018)
  143. Theoretical issues in deep networks (2020)
  144. The dual information bottleneck (2020) — link
  145. No free lunch theorems for optimization (1997)
  146. Greedy function approximation: a gradient boosting machine (2001)
  147. CatBoost: unbiased boosting with categorical features (2018)
  148. Tabular data: Deep learning is not all you need (2022)
  149. Openml benchmarking suites (2017) — link
  150. Tabpfn: A transformer that solves small tabular classification problems in a second (2022) — link
  151. UCI machine learning repository (2017)
  152. Why do tree-based models still outperform deep learning on tabular data? (2022) — link
  153. Tabnet: Attentive interpretable tabular learning (2021)
  154. High-dimensional data analysis: The curses and blessings of dimensionality (2000)
  155. Why and when can deep-but not shallow-networks avoid the curse of dimensionality: a review (2017)
  156. Data mining: concepts and techniques (2022)
  157. Feature selection: A data perspective (2017)
  158. Nested hierarchies in planar graphs (2011)
  159. A balanced approach to the multi-class imbalance problem (2013)
  160. Practical text mining and statistical analysis for non-structured text data applications (2012)
  161. A solution to the curse of dimensionality problem in pairwise scoring techniques (2006)
  162. Fundamentals of machine learning for predictive data analytics: algorithms, worked examples, and case studies (2020)
  163. Gini diversity index, hamming distance and curse of dimensionality (2005)
  164. Assessing the accuracy of prediction algorithms for classification: an overview (2000)
  165. Comparing two K-category assignments by a K-category correlation coefficient (2004)
  166. Effective dimension reduction methods for tumor classification using gene expression data (2003)
  167. Energy and policy considerations for deep learning in NLP (2019) — link
  168. Carbon emissions and large neural network training (2021) — link
  169. Deeplob: Deep convolutional neural networks for limit order books (2019)
  170. A comparison of MCC and CEN error measures in multi-class prediction (2012)
  171. Propensity score methodology for confounding control in health care utilization databases (2013)
  172. Digital medicine and the curse of dimensionality (2021)
  173. Novel HealthCare Framework for Cardiac Arrest With the Application of AI Using ANN (2021)
  174. Combining trajectory optimization, supervised machine learning, and model structure for mitigating the curse of dimensionality in the control of bipedal robots (2019)
  175. Utilizing high-dimensional features for real-time robotic applications: Reducing the curse of dimensionality for recursive bayesian estimation (2016)
  176. Binarising SIFT-descriptors to reduce the curse of dimensionality in histogram-based object recognition (2009)
  177. A neural basis computational model of emotional brain for online visual object recognition (2014)
  178. Multipose audio-visual speech recognition (2011)
  179. Sentiment analysis: a review and comparative analysis over social media (2020)
  180. Fusing social media cues: personality prediction from twitter and instagram (2016)
  181. The curse of dimensionality in data mining and time series prediction (2005)
  182. Brownian bridge and principal component analysis: towards removing the curse of dimensionality (2007)
  183. Deep reinforcement learning for market making in corporate bonds: beating the curse of dimensionality (2019)
  184. Feature extraction: foundations and applications (2008)
  185. McTwo: a two-step feature selection algorithm based on maximal information coefficient (2016)
  186. Big data storage technologies: a survey (2017)
  187. Big data: issues, challenges, tools and good practices (2013)
  188. Big data storage and challenges (2014)
  189. Big data storage (2016)
  190. From databases to big data (2012)
  191. Experiences with the model-based generation of Big Data pipelines (2017)
  192. Building pipelines for heterogeneous execution environments for big data processing (2016)
  193. What do we need to build explainable AI systems for the medical domain? (2017) — link
  194. Explainable deep learning models in medical image analysis (2020)
  195. Explainable machine learning of the underlying physics of high-energy particle collisions (2022)
  196. Explainable artificial intelligence for 6G: Improving trust between human and machine (2020)
  197. Learning a functional control for high-frequency finance (2020) — link
  198. Supervised feature selection: A tutorial. (2015)
  199. A review of unsupervised feature selection methods (2020)
  200. A survey on semi-supervised feature selection methods (2017)
  201. Infinite feature selection (2015)
  202. Topological regularization with information filtering networks (2022)
  203. Hierarchical structure in financial markets (1999)
  204. A tool for filtering information in complex systems (2005)
  205. Learning from co-expression networks: possibilities and challenges (2016)
  206. A review of two decades of correlations, hierarchies, networks and clustering in financial markets (2021)
  207. Newsweeder: Learning to filter netnews (1995)
  208. Feature selection: A data perspective (2018)
  209. Columbia object image library (coil-100) (1996)
  210. Parameterisation of a stochastic model for human face identification (1994)
  211. The CMU pose, illumination, and expression (PIE) database (2002)
  212. Eigenfaces vs. fisherfaces: Recognition using class specific linear projection (1997)
  213. A database for handwritten text recognition research (1994)
  214. Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays (1999)
  215. Molecular classification of cancer: class discovery and class prediction by gene expression monitoring (1999)
  216. Competitive baseline methods set new standards for the NIPS 2003 feature selection benchmark (2007)
  217. Infinite Feature Selection
  218. Feature Selection Datasets, Arizona State University
  219. UCI Machine Learning Repository (2017) — link
  220. Topology of correlation-based minimal spanning trees in real and model markets (2003)
  221. Networks of equities in financial markets (2004)
  222. High-frequency cross-correlation in a set of stocks (2001)
  223. Scikit-learn: Machine Learning in P ython (2011)
  224. Computational study of the US stock market evolution: a rank correlation-based network model (2013)
  225. Anatomy of a stablecoin’s failure: The Terra-Luna case (2022)
  226. Network structure of the Wisconsin Schizotypy Scales–Short Forms: Examining psychometric network filtering approaches (2018)
  227. Complex networks on hyperbolic surfaces (2005)
  228. Parsimonious modeling with information filtering networks (2016)
  229. Network filtering for big data: Triangulated maximally filtered graph (2017)
  230. Portfolio optimization with sparse multivariate modeling (2022)
  231. Dynamic portfolio optimization with inverse covariance clustering (2022)
  232. Quantifying impact and response in markets using information filtering networks (2022)
  233. NetworkToolbox: Methods and Measures for Brain, Cognitive, and Psychometric Network Analysis in R. (2018)
  234. Correlation-based biological networks (2008)
  235. Hierarchical information clustering by means of topologically embedded graphs (2012)
  236. Multi-modal functional MRI to explore placental function over gestation (2019)
  237. Genetic, epigenetic, and environmental factors controlling oxytocin receptor gene expression (2021)
  238. Probabilistic graphical models: principles and techniques (2009)
  239. Deep learning modeling of limit order book: A comparative perspective (2020) — link
  240. Infinite feature selection: a graph-based feature filtering approach (2020)
  241. A mathematical theory of adaptive control processes (1959)
  242. LIII. On lines and planes of closest fit to systems of points in space (1901)
  243. Comparison of the predicted and observed secondary structure of T4 phage lysozyme (1975)
  244. Combinatorial optimization: algorithms and complexity (1998)
  245. Approximate statistical tests for comparing supervised classification learning algorithms (1998)
  246. Correlations among centrality measures in complex networks (2006)
  247. How correlated are network centrality measures? (2008)
  248. Natural language processing (2020)
  249. A commentary of GPT-3 in MIT Technology Review 2021 (2021)
  250. A review of deep learning in image recognition (2017)
  251. Deep learning for audio signal classification (2020)
  252. Simplicial complexes: higher-order spectral dimension and dynamics (2020)
  253. Simplicial complexes and complex systems (2018)
  254. Multivariate analysis (1979)
  255. Noise dressing of financial correlation matrices (1999)
  256. Random matrix approach to cross correlations in financial data (2002)
  257. The broad view of cluster analysis (1973)
  258. Introduction to graph theory (2001)
  259. Data clustering and noise undressing of correlation matrices (2001)
  260. Algorithms of maximum likelihood data clustering with applications (2002)
  261. Spanning trees and bootstrap reliability estimation in correlation-based networks (2007)
  262. Bootstrap methods: another look at the jackknife (1992)
  263. Bootstrap confidence levels for phylogenetic trees (1996)
  264. A review of feature selection and its methods (2019)
  265. Topological Feature Selection (2023)
  266. Topological Portfolio Selection and Optimization — → 2310.14881
  267. Towards end-to-end speech recognition with recurrent neural networks (2014)
  268. Deep speech 2: End-to-end speech recognition in english and mandarin (2016)
  269. Exploring the limits of language modeling (2016) — link
  270. Google’s neural machine translation system: Bridging the gap between human and machine translation (2016) — link
  271. Sparsity in deep learning: Pruning and growth for efficient inference and training in neural networks (2021)
  272. Distilling the knowledge in a neural network (2015) — link
  273. Neural architecture search: A survey (2019)
  274. Model compression (2006)
  275. Low-rank matrix factorization for deep neural network training with high-dimensional output targets (2013)
  276. Learning efficient tensor representations with ring-structured networks (2019)
  277. Reduced-size neural networks through singular value decomposition and subset selection (1993)
  278. Binaryconnect: Training deep neural networks with binary weights during propagations (2015)
  279. Quantized neural networks: Training neural networks with low precision weights and activations (2017)
  280. Quantization and training of neural networks for efficient integer-arithmetic-only inference (2018)
  281. Deep compression: Compressing deep neural networks with pruning, trained quantization and huffman coding (2015) — link
  282. DeepSZ: A novel framework to compress deep neural networks by using error-bounded lossy compression (2019)
  283. Neural parameter allocation search (2020) — link
  284. Learning both weights and connections for efficient neural network (2015)
  285. Dynamic network surgery for efficient dnns (2016)
  286. Good subnetworks provably exist: Pruning via greedy forward selection (2020)
  287. Pruning filters for efficient convnets (2016) — link
  288. Pruning neural networks at initialization: Why are we missing the mark? (2020) — link
  289. The lottery ticket hypothesis: Finding sparse, trainable neural networks (2018) — link
  290. Progressive skeletonization: Trimming more fat from a network at initialization (2020) — link
  291. Lightgbm: A highly efficient gradient boosting decision tree (2017)
  292. Feature selection with decision tree criterion (2005)
  293. Gradient boosting neural networks: Grownet (2020) — link
  294. The tree ensemble layer: Differentiability meets conditional computation (2020)
  295. Tabtransformer: Tabular data modeling using contextual embeddings (2020) — link
  296. Self-normalizing neural networks (2017)
  297. Deep neural decision forests (2015)
  298. Neural oblivious decision ensembles for deep learning on tabular data (2019) — link
  299. An image is worth 16x16 words: Transformers for image recognition at scale (2020) — link
  300. Autoint: Automatic feature interaction learning via self-attentive neural networks (2019)
  301. Saint: Improved neural networks for tabular data via row attention and contrastive pre-training (2021) — link
  302. Latent cross: Making use of context in recurrent recommender systems (2018)
  303. GLUE: A multi-task benchmark and analysis platform for natural language understanding (2018) — link
  304. Learning deep transformer models for machine translation (2019) — link
  305. Regularization is all you need: Simple neural nets can excel on tabular data (2021) — link
  306. Regularization learning networks: deep learning for tabular datasets (2018)
  307. baosenguo/kaggle-moa-2nd-place-solution (2021)
  308. Converting tabular data into images for deep learning with convolutional neural networks (2021)
  309. Statistical comparisons of classifiers over multiple data sets (2006)
  310. When Do Neural Nets Outperform Boosted Trees on Tabular Data? (2023) — link
  311. Revisiting pretraining objectives for tabular deep learning (2022) — link
  312. Revisiting deep learning models for tabular data (2021)
  313. Algorithms for hyper-parameter optimization (2011)
  314. UCL CS HPC Cluster (2023)
  315. Optimal classifier for imbalanced data using Matthews Correlation Coefficient metric (2017)
  316. The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation (2020)
  317. Homological Neural Networks: A Sparse Architecture for Multivariate Complexity (2023) — link
  318. Big bird: Transformers for longer sequences (2020)
  319. Longformer: The long-document transformer (2020) — link
  320. Simplicial convolutional neural networks (2022)
  321. Simplicial neural networks (2020) — link
  322. OpenML: A benchmarking layer on top of OpenML to quickly create, download, and share systematic benchmarks (2021) — link
  323. On information and sufficiency (1951)
  324. A greedy random adaptive search procedure for the weighted maximal planar graph problem (2003)
  325. Graph theory and its applications (2018)
  326. Information theory for continuous systems (1993)
  327. Modeling complex systems (2010)
  328. Deep Limit Order Book Forecasting — → 2403.09267
  329. itransformer: Inverted transformers are effective for time series forecasting (2023) — link
  330. Market microstructure in practice (2018)
  331. Network filtering for big data: Triangulated maximally filtered graph (2016)
  332. Dynamical networks from correlations (2006)
  333. Correlation based networks of equity returns sampled at different time horizons (2007)
  334. Cross-impact of order flow imbalance in equity markets (2023)

5 of 342 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.