Paper: arXiv 2408.12839

Abstract

Granger causality can uncover the cause and effect relationships in financial networks. However, such networks can be convoluted and difficult to interpret, but the Helmholtz-Hodge-Kodaira decomposition can split them into a rotational and gradient component which reveals the hierarchy of Granger causality flow. Using Kenneth French’s business sector return time series, it is revealed that during the Covid crisis, precious metals and pharmaceutical products are causal drivers of the financial network. Moreover, the estimated Granger causality network shows a high connectivity during crisis which means that the research presented here can be especially useful to better understand crises in the market by revealing the dominant drivers of the crisis dynamics.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematical concepts like Granger causality, Helmholtz-Hodge-Kodaira decomposition, and PCA, with dense derivations, but is grounded in a specific financial dataset (Kenneth French’s 49 sectors) with detailed estimation procedures and empirical results during the Covid crisis.

Research Flowchart

  flowchart TD
  Start["Research Goal: Analyze the hierarchical structure of causality in financial markets during the Covid crisis"] --> InputData["Input: Kenneth French business sector return time series"]
  InputData --> GC["Methodology: Construct Granger Causality Network"]
  GC --> Decomp["Computational Process: Helmholtz-Hodge-Kodaira Decomposition"]
  Decomp --> Comp1["Gradient Component (Potential Flow)"]
  Decomp --> Comp2["Rotational Component (Cyclic Flow)"]
  Comp1 --> Hierarchy["Output: Causal Hierarchy Extraction"]
  Comp2 --> Hierarchy
  Hierarchy --> Findings["Key Findings: Precious metals & pharmaceuticals as causal drivers; High network connectivity during crisis"]

Cited References (388)

  1. Portfolio Selection (1952) — link
  2. yfinance 0.1.70 (2022) — link
  3. Sector Classification (2018)
  4. Introduction to Econophysics: Contemporary Approaches with Python Simulations (2021) — link
  5. Local normalization. Uncovering correlations in non-stationary financial time series (2010) — link
  6. From Clustering to Cluster Explanations via Neural Networks (2021) — link
  7. Some methods for classification and analysis of multivariate observations (1967)
  8. Explainable AI (2019) — link
and 380 more
  1. Layer-Wise Relevance Propagation: An Overview (2019) — link
  2. Dissecting financial markets: sectors and states (2002) — link
  3. Learning Important Features Through Propagating Activation Differences (2017) — link
  4. Top-Down Neural Attention by Excitation Backprop (2018) — link
  5. Interpreting individual classifications of hierarchical networks (2013) — link
  6. Methods for interpreting and understanding deep neural networks (2018) — link
  7. pandas-dev/pandas: Pandas (2020) — link
  8. D ata S tructures for S tatistical C omputing in P ython ( 2010 ) — link
  9. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python (2020) — link
  10. The application of cluster analysis in strategic management research: an analysis and critique (1996) — link
  11. Bayesian on-line anticipation of critical transitions (2021) — link
  12. XAI in the Financial Sector (2020) — link
  13. Artificial Inteligence market and capital flows - AI and the financial sector at crossroads (2021) — link
  14. Interpretable Machine Learning (2022) — link
  15. Big data meets artificial intelligence (2018) — link
  16. Keras (2015) — link
  17. TensorFlow : Large-Scale Machine Learning on Heterogeneous Systems (2015) — link
  18. Revealing drivers and risks for power grid frequency stability with explainable AI (2021) — link
  19. What has econophysics ever done for us? (2013) — link
  20. A map of the Brazilian stock market (2012) — link
  21. Network analysis of global stock markets at the beginning of the coronavirus disease (Covid-19) outbreak (2020) — link
  22. A complex network perspective of world stock markets: Synchronization and volatility (2012) — link
  23. Correlation of financial markets in times of crisis (2012) — link
  24. Degree of correlation inside a financial market (1997) — link
  25. Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series (1999) — link
  26. The Number of Factors in Security Returns (1989) — link
  27. Hierarchical structure in financial markets (1999) — link
  28. Econophysics: making sense of a chimera (2021) — link
  29. A Review of Two Decades of Correlations, Hierarchies, Networks and Clustering in Financial Markets (2021) — link
  30. Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead (2019) — link
  31. Detecting Recurrence Domains of Dynamical Systems by Symbolic Dynamics (2013) — link
  32. Uncovering the dynamics of correlation structures relative to the collective market motion (2020) — link
  33. A new attempt to identify long-term precursors for endogenous financial crises in the market correlation structures (2022) — link
  34. New Collectivity Measures for Financial Covariances and Correlations (2022) — link
  35. Bayesian analysis of climate change impacts in phenology (2004) — link
  36. Detection of fixed points in spatiotemporal signals by clustering method (2000) — link
  37. Complexity Explained (2022) — link
  38. Scaling behaviour in the dynamics of an economic index (1995)
  39. Theory for long memory in supply and demand (2005) — link
  40. Inferring Microscopic Financial Information from the Long Memory in Market-Order Flow: A Quantitative Test of the Lillo-Mike-Farmer Model (2023) — link
  41. An Introduction to Econophysics (2000)
  42. Th'eorie de la sp'eculation (1900)
  43. The Pricing of Options and Corporate Liabilities (1973)
  44. Theory of Rational Option Pricing (1973)
  45. Evidence of Markov properties of high frequency exchange rate data (2001) — link
  46. A Nonlinear Model of the Term Structure of Interest Rates (1997) — link
  47. A Langevin Approach to Stock Market Fluctuations and Crashes (1998) — link
  48. Parameter Estimation of a Generalized Langevin Equation of Market Price (2002) — link
  49. Kinetic theory for financial Brownian motion from microscopic dynamics (2018) — link
  50. Forecast model for financial time series: An approach based on harmonic oscillators (2020)
  51. The Inverted Parabola World of Classical Quantitative Finance: Non-Equilibrium and Non-Perturbative Finance Perspective (2020) — link
  52. “Quantum Equilibrium-Disequilibrium”: Asset price dynamics, symmetry breaking, and defaults as dissipative instantons (2019) — link
  53. Machine Learning in Finance (2020) — link
  54. Estimation of Kramers-Moyal coefficients at low sampling rates (2011)
  55. Approaching complexity by stochastic methods: From biological systems to turbulence (2011)
  56. Maximum likelihood estimation of drift and diffusion functions (2007)
  57. Discovering governing equations from data by sparse identification of nonlinear dynamical systems (2016)
  58. Ensemble- SINDy : Robust sparse model discovery in the low-data, high-noise limit, with active learning and control (2022)
  59. Bayesian on-line anticipation of critical transitions (2021)
  60. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering (2000)
  61. Information Theory and an Extension of the Maximum Likelihood Principle (1998) — link
  62. Pricing with a smile (1994)
  63. A closed-form solution for options with stochastic volatility with applications to bond and currency options (1993)
  64. Efficient Bayesian estimation of the generalized L angevin equation from data (2021) — link
  65. Non-parametric estimation of a Langevin model driven by correlated noise (2021)
  66. Bayesian probability theory: applications in the physical sciences (2014)
  67. Monte Carlo sampling methods using Markov chains and their applications (1970) — link
  68. emcee: The MCMC Hammer (2013) — link
  69. Numerical solution of stochastic differential equations (2013)
  70. Analysis of data sets of stochastic systems (1998) — link
  71. Extracting model equations from experimental data (2000) — link
  72. How to Quantify Deterministic and Random Influences on the Statistics of the Foreign Exchange Market (2000) — link
  73. Quantifying the Beta Estimation Bias and its Implications for Empirical Asset Pricing (2022)
  74. Liquidity measurement problems in fast, competitive markets: Expensive and cheap solutions (2014)
  75. Symmetry and financial markets (2022) — link
  76. Quantifying resilience and the risk of regime shifts under strong correlated noise (2022) — link
  77. Presidential Address: Discount Rates (2011) — link
  78. Financial market complexity (2003)
  79. Physique sociale (1975)
  80. The time interpretation of expected utility theory (2021) — link
  81. Insurance makes wealth grow faster (2017) — link
  82. The time resolution of the St Petersburg paradox (2011) — link
  83. Ergodicity Economics Lecture Notes (2018)
  84. Unfair and Anomalous Evolutionary Dynamics from Fluctuating Payoffs (2018) — link
  85. The ergodicity solution of the cooperation puzzle (2022) — link
  86. Evaluating gambles using dynamics (2016) — link
  87. Insurance as an ergodicity problem (2023)
  88. Insurance as an ergodicity problem (2023)
  89. LMLhub/AAS_editorial_figures_July2023: v1.0.0 initial release (2023) — link
  90. Stable cooperation emerges in stochastic multiplicative growth (2023) — link
  91. Cooperation in an Uncertain World: For the Maasai of East Africa, Need-Based Transfers Outperform Account-Keeping in Volatile Environments (2016) — link
  92. Risk-Pooling and Herd Survival: An Agent-Based Model of a Maasai Gift-Giving System (2011) — link
  93. Having herds: Pastoral herd growth and household economy (1976)
  94. Dynamic models of segregation (1971) — link
  95. Evolutionary games and spatial chaos (1992) — link
  96. Five Rules for the Evolution of Cooperation (2006) — link
  97. The influence of ergodicity on risk affinity of timed and non-timed respondents (2022) — link
  98. Human decision-making in a non-ergodic additive environment (2023) — link
  99. Theories of Poverty Traps and Anti-Poverty Policies (2015) — link
  100. Beitrag zur Theorie des Ferromagnetismus (1925) — link
  101. Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition (1944) — link
  102. Ergodicity-breaking reveals time optimal decision making in humans (2021) — link
  103. Opinion Evolution in Closed Community (2000) — link
  104. Social applications of two-dimensional Ising models (2008) — link
  105. Physics and financial economics (1776–2014): puzzles, Ising and agent-based models (2014) — link
  106. Is salary just a negative insurance premium? (2024)
  107. Evolutionary Dynamics in Changing Environments (2018) — link
  108. Synergetic Economics (1991) — link
  109. Self-organization in Economic Systems (2007) — link
  110. Economics and the Self-Organisation Approach: Alfred Marshall Revisited? (1993) — link
  111. Origins and Persistence of Economic Inequality (2010) — link
  112. The theory of risk aversion (1971)
  113. Asymmetric Information in Insurance: General Testable Implications (2006)
  114. Are risk preferences optimal? (2023) — link
  115. Asset Prices in an Exchange Economy (1978) — link
  116. Unlearnable Games and “Satisficing’’ Decisions: A Simple Model for a Complex World (2024) — link
  117. Three-state opinion model with mobile agents (2023) — link
  118. Crises and Collective Socio-Economic Phenomena: Simple Models and Challenges (2013) — link
  119. Echo chambers in the Ising model and implications on the mean magnetization (2022) — link
  120. Ising models to study effects of risk aversion in socially interacting individuals (2023) — link
  121. Rise of nations: Why do empires expand and fall? (2020) — link
  122. Der Weg zur Knechtschaft (2017)
  123. Fractals and Scaling in Finance (1997) — link
  124. The index of general nonlinear D A E S (1995)
  125. Clinical implications of dysregulated cytokine production (2000) — link
  126. Quasimonotonicity, regularity and duality for nonlinear systems of partial differential equations (1995)
  127. Algorithms for C omputer A lgebra (1992)
  128. Software engineering—from auxiliary to key technologies (1992)
  129. Conductive P olymers (1981)
  130. Neuromuscular blocking drugs in man (1976)
  131. Isolation and characterization of plasmid deoxyribonucleic acid from Streptomyces fradiae (1978)
  132. Global integrated drought monitoring and prediction system (GIDMaPS) data sets (2014)
  133. Quantum scissors: teleportation of single-mode optical states by means of a nonlocal single photon (2002)
  134. Mixing induced CP asymmetries in inclusive B decays (1997) — link
  135. deep SIP : deep learning of S upernova I a P arameters (2020) — link
  136. Applying graphs and complex networks to football metric interpretation (2018) — link
  137. Complex network study of Brazilian soccer players (2004) — link
  138. Networks as a novel tool for studying team ball sports as complex social systems (2011) — link
  139. Handbook of Graphs and Networks (2005)
  140. Large Scale Structure and Dynamics of Complex Networks (2007)
  141. Soccer: Is scoring goals a predictable Poissonian process? (2010) — link
  142. On the dependency of soccer scores – a sparse bivariate Poisson model for the UEFA European football championship 2016 (2018) — link
  143. Topology of the world trade web (2003) — link
  144. Sportökonomische Auswirkungen der COVID-19-Pandemie am Beispiel der Fußball-Bundesligen (2021) — link
  145. The real impact of COVID on the football players’ transfer market (2020) — link
  146. Game Over? Die Auswirkungen der Corona-Pandemie auf den Profisport (2021)
  147. The German Bundesliga clubs and their future—an outlook on the robustness of the clubs in times of Covid-19 — link
  148. transfers (2021)
  149. Collective dynamics of `small-world’ networks (1998) — link
  150. Clustering in complex directed networks (2007) — link
  151. The Architecture of Complex Weighted Networks: Measurements and Models (2007)
  152. Exploring network structure, dynamics, and function using NetworkX (2008)
  153. Network ‘Small-World-Ness’: A Quantitative Method for Determining Canonical Network Equivalence (2008) — link
  154. Network visualizations with Pyvis and VisJS (2020)
  155. Mathematical Formulation of Multilayer Networks (2013) — link
  156. A Deep Stochastic Model for Detecting Community in Complex Networks (2017)
  157. The behaviour of share returns of football clubs: An econophysics approach (2017) — link
  158. Emergence of Scaling in Random Networks (1999) — link
  159. The Ubiquity of Small-World Networks (2011) — link
  160. Hidden power law patterns in the top European football leagues (2013) — link
  161. Robustness of football passing networks against continuous node and link removals (2021) — link
  162. Clustering algorithm for formations in football games (2019) — link
  163. Win-stay lose-shift strategy in formation changes in football (2015) — link
  164. Statistical properties of position-dependent ball-passing networks in football games (2014) — link
  165. On the shortest spanning subtree of a graph and the traveling salesman problem (1956) — link
  166. Self-organization of dragon king failures (2018) — link
  167. Curtailing cascading failures (2017) — link
  168. Cascade Control and Defense in Complex Networks (2004) — link
  169. transfermarkt
  170. Error and attack tolerance of complex networks (2000) — link
  171. The impact of turbulent renewable energy production on power grid stability and quality (2017) — link
  172. Effect of network topology and node centrality on trading (2020) — link
  173. Random graphs with arbitrary degree distributions and their applications (2001) — link
  174. Ising-based model of opinion formation in a complex network of interpersonal interactions (2006) — link
  175. Historical Dynamics: Why States Rise and Fall (2003)
  176. Der Untergang des Abendlandes (1918)
  177. Seshat: The Global History Databank (2015) — link
  178. Transition to agriculture and first state presence (2021) — link
  179. Quantitative historical analysis uncovers a single dimension of complexity that structures global variation in human social organization (2018) — link
  180. Explaining the Rise of Moralizing Religions: A test of competing hypotheses using the Seshat Databank (2019) — link
  181. Explaining the rise of moralizing religions: a test of competing hypotheses using the Seshat Databank (2022) — link
  182. seshatdb (Equinox Packaged Data) (2022) — link
  183. Applied Logistic Regression (2000)
  184. Notice sur la loi que la population poursuit dans son accroissement (1838)
  185. The emergence of pristine states (2016)
  186. Territorial expansion and primary state formation (2010) — link
  187. Tempo and Mode in Cultural Macroevolution (2021) — link
  188. Disentangling the evolutionary drivers of social complexity: A comprehensive test of hypotheses (2022) — link
  189. An integrative approach to estimating productivity in past societies using Seshat: Global History Databank (2021) — link
  190. Rise of the war machines: Charting the evolution of military technologies from the Neolithic to the Industrial Revolution (2021) — link
  191. Characteristic time scales for diffusion processes through layers and across interfaces (2018) — link
  192. Characteristic Chemical Time Scales for Reactive Flow Modeling (2021) — link
  193. On Estimation of a Probability Density Function and Mode (1962) — link
  194. Remarks on Some Nonparametric Estimates of a Density Function (1956) — link
  195. An Introduction to the Bootstrap (1994) — link
  196. Kulturmorphologie und Willensfreiheit (2018)
  197. Scale and information-processing thresholds in Holocene social evolution (2020) — link
  198. Cooperation and Collective Action in the Cultural Evolution of Complex Societies — link
  199. Arise ‘cliodynamics’ — link
  200. Collaborative Historical Information Analysis
  201. An Introduction to Seshat — link
  202. A Macroscope for Global History. Seshat Global History Databank: a methodological overview — link
  203. Social Scale and Collective Computation (2022) — link
  204. Testing the Big Gods hypothesis with global historical data: a review and “retake” (2022) — link
  205. The Ancient Indus Valley: New Perspectives (2008)
  206. From Nausharo to Pirak: Continuity and change in the Kachi/Bolan Region from the 3rd to the 2nd Millennium BC (1995)
  207. Longshan (2001)
  208. The Longshan culture in central Henan province, c. 2600–1900 BC (2013)
  209. The Chinese Neolithic : Trajectories to Early States (2005)
  210. Longshan-era urbanism: The role of cities in predynastic China (1999) — link
  211. Man Makes Himself (1936)
  212. The Evolution of Culture (1959)
  213. Origins of the state and civilization (1975)
  214. From chiefdom to archaic state: Hawai’i in comparative and historical context (2010)
  215. Multiple imputation for nonresponse in surveys (2004)
  216. History by the numbers? (2018) — link
  217. Reply to Tosh et al.: Quantitative analyses of cultural evolution require engagement with historical and archaeological research (2018) — link
  218. Dimension reduction for stochastic dynamical systems forced onto a manifold by large drift: a constructive approach with examples from theoretical biology (2017) — link
  219. Synergetik (1990)
  220. The Equinox2020 Seshat Data Release (2020)
  221. Seshat: Equinox Release with Continuous Polities (2023) — link
  222. The vulnerability of aging states: A survival analysis across premodern societies (2023) — link
  223. A Dynamic Network Model of Societal Complexity and Resilience Inspired by Tainter’s Theory of Collapse (2024) — link
  224. AIC model selection and multimodel inference in behavioral ecology: some background, observations, and comparisons (2010)
  225. The Use of Knowledge in Society (1945)
  226. Why stock markets crash (2004)
  227. Tipping points in macroeconomic agent-based models (2015) — link
  228. Oscillators that sync and swarm (2017) — link
  229. Introduction to Superconductivity: v. 1 (2004)
  230. Self-organized criticality: An explanation of the 1/fnoise (1987) — link
  231. Predictability of catastrophic events: Material rupture, earthquakes, turbulence, financial crashes, and human birth (2002) — link
  232. Random superharmonic and subharmonic response: Multiple time scaling of a duffing oscillator (1988) — link
  233. Computational multiscale modeling of fluids and solids (2010)
  234. Numerical Simulation of Van der Pol Equation Using Multiple Scales Modified Lindstedt–Poincare Method (2020) — link
  235. Efficient Capital Markets: A Review of Theory and Empirical Work (1970) — link
  236. Nonlinear dynamics and statistics (2001)
  237. Analysis and data-based reconstruction of complex nonlinear dynamical systems (2020)
  238. Big data: the end of the scientific method? (2019) — link
  239. Probability in physics (2019)
  240. LII . An essay towards solving a problem in the doctrine of chances. (1763) — link
  241. Data analysis (2006)
  242. Introduction to Artificial Intelligence (2024)
  243. Practical Bayesian Inference: A Primer for Physical Scientists (2017)
  244. Scikit-learn: Machine Learning in P ython (2011)
  245. Schemdraw
  246. A logical calculus of the ideas immanent in nervous activity (1943) — link
  247. Unmasking Clever Hans Predictors and Assessing What Machines Really Learn (2019) — link
  248. “Why Should I Trust You?”: Explaining the Predictions of Any Classifier (2016) — link
  249. A Unified Approach to Interpreting Model Predictions (2017) — link
  250. A value for n-person games (1988) — link
  251. Escape from model-land (2019) — link
  252. Escape from model land (2022)
  253. From Ordinary Differential Equations to Structural Causal Models: the deterministic case (2013) — link
  254. Learning driver-response relationships from synchronization patterns (2000) — link
  255. Detecting Causality in Complex Ecosystems (2012) — link
  256. Generalized Theorems for Nonlinear State Space Reconstruction (2011) — link
  257. Investigating Causal Relations by Econometric Models and Cross-spectral Methods (1969)
  258. Transient and equilibrium causal effects in coupled oscillators (2018) — link
  259. Estimating stable fixed points and Langevin potentials for financial dynamics — → 2309.12082
  260. Causal Inference in Statistics: A Primer (2016)
  261. Causal Network Inference by Optimal Causation Entropy (2015) — link
  262. From Clustering to Cluster Explanations via Neural Networks (2022) — link
  263. Noise Dressing of Financial Correlation Matrices (1999) — link
  264. B ayesian P robability T heory (2014)
  265. When instability makes sense (2005) — link
  266. Energy consumption and economic growth: New evidence from the OECD countries (2018) — link
  267. Electricity Consumption and Economic Growth: Evidence from Poland (2014)
  268. Cluster-based network modeling \textemdash From snapshots to complex dynamical systems (2021) — link
  269. Hands-on machine learning with scikit-learn, keras, and TensorFlow (2019)
  270. Generating random correlation matrices by the simple rejection method: Why it does not work (2014) — link
  271. Algorithms of maximum likelihood data clustering with applications (2002) — link
  272. Explainable AI for High Energy Physics (2022) — link
  273. Lessons on interpretable machine learning from particle physics (2022) — link
  274. Identifying States of a Financial Market (2012) — link
  275. Stability and hierarchy of quasi-stationary states: financial markets as an example (2015)
  276. Dynamics of quasi-stationary systems: Finance as an example (2015) — link
  277. statsmodels: Econometric and statistical modeling with python (2010)
  278. New collectivity measures for financial covariances and correlations (2022)
  279. Approaching complexity by stochastic methods: From biological systems to turbulence (2011) — link
  280. Indispensable Finite Time Corrections for Fokker-Planck Equations from Time Series Data (2001)
  281. Comment on ``Indispensable Finite Time Corrections for Fokker-Planck Equations from Time Series Data’’ (2002)
  282. Ragwitz and Kantz Reply: (2002)
  283. Bayesian analysis of climate change impacts in phenology (2004)
  284. Transport, Collective Motion, and Brownian Motion (1965) — link
  285. Efficient Bayesian estimation of a non-Markovian Langevin model driven by correlated noise (2022) — link
  286. Monte Carlo sampling methods using Markov chains and their applications (1970) — link
  287. Introducing Memory in Coarse-Grained Molecular Simulations (2021) — link
  288. Stochastic modelling of a noise-driven global instability in a turbulent swirling jet (2021) — link
  289. Reconstruction of the modified discrete Langevin equation from persistent time series (2016) — link
  290. Bifurcation Routes to Volatility Clustering under Evolutionary Learning (2008) — link
  291. Volatility clustering: A nonlinear theoretical approach (2016) — link
  292. Changes in Cross-Correlations as an Indicator for Systemic Risk (2012) — link
  293. S&P slashes Spain’s debt rating (2010) — link
  294. Spanish and Italian Bond Yields Drop on E.C.B. Buying (2011) — link
  295. IMF Survey: Europe and IMF Agree €110 Billion Financing Plan With Greece (2022)
  296. Financial assistance to Portugal (2023)
  297. Cheer Fades as Stocks Plunge 9 (2008)
  298. Fed: Emergency cut (2008)
  299. Banks ask for crisis funds for eastern Europe (2009)
  300. Oil futures extend gains amid unrest (2011)
  301. Arab Spring.pro-democracy protests (2023)
  302. Standard & Poor’s downgrade Greek credit rating to junk status (2010)
  303. Euro falls to four-year low against dollar as its reserve status dips (2010)
  304. The 2010 ``flash crash’’: how it unfolded (2015)
  305. Dow drops 324 points as euro sinks (2010)
  306. U.S. Imports from Venezuela of Crude Oil and Petroleum Products (2008)
  307. Daily Treasury Par Yield Curve Rates (2023)
  308. Daily Treasury Par Yield Curve Rates (2023)
  309. The Great Recession and Its Aftermath (2013)
  310. Financial crisis: US stock markets suffer worst week on record (2008)
  311. Trading halted for first time since 2008 over pandemic (2020)
  312. Iceland markets plummet (2008)
  313. D otcom B ubble (2019)
  314. ECONStats. Equity Index Data. NASDAQ Composite Index
  315. The great bond massacre (Fortune, 1994) (2013)
  316. IMF W orking P aper. T he R ussian F inancial C risis and its C onsequences for C entral A sia. (2001)
  317. A sian F inancial C risis. July 1997-December 1998. (2001)
  318. 10 T equila H angover: T he M exican P eso C risis and I ts A ftermath (2010-2021)
  319. I nflation fears punish D ow (1999)
  320. 2008 Financial Crisis Timeline (2022)
  321. The 9/11 C ommission R eport (2004)
  322. U.S. Conventional Gas and Crude Oil, Prices WTI - Cushing Oklahoma (2023)
  323. 2003-2008 O il P rice S hock: C hanging E ffects of O il S hocks on the E conomy (2018)
  324. Venezuelan general strike extended (2002)
  325. G eborgtes V ertrauen auch nach zehn J ahren D auerfinanzkrise (2017)
  326. Aug. 9, 2007: The Day the Mortgage Crisis Went Global (2017)
  327. The Lehman Brothers Bankruptcy A: Overview (2014) — link
  328. What drove the 2003–2006 house price boom and subsequent collapse? Disentangling competing explanations (2021) — link
  329. Global financial turmoil and emerging market economies: Major contagion and a shocking loss of wealth? (2009)
  330. anti CP y (2021) — link
  331. anti CPy ’s documentation (2021) — link
  332. Nonlinear dynamics and chaos. With Applications to Physics, Biology, Chemistry and Engineering. (2015)
  333. The Characteristic Time Scale of Cultural Evolution (2023) — link
  334. The Long Waves in Economic Life (1935)
  335. Konjunkturzyklen (1961)
  336. World Economic Outlook (2008) — link
  337. S&P500 Mean Correlation Time Series (1992-2012) (2023)
  338. Das Kapital - Kritik der politischen Ökonomie (2014)
  339. Trends and cycles in economic time series: A Bayesian approach (2007) — link
  340. Time Scales and Mechanisms of Economic Cycles: A Review of Theories of Long Waves 1 (2013) — link
  341. Efficient Multi-Change Point Analysis to decode Economic Crisis Information from the S&P500 Mean Market Correlation (2023) — link
  342. Identifying dominant industrial sectors in market states of the S&P 500 financial data (2023) — link
  343. PhD Thesis on the Anticipation of Critical Transitions in Complex Systems (forthcoming) (2024)
  344. Physical approach to complex systems (2012) — link
  345. Turbulent cascades in foreign exchange markets (1996) — link
  346. Volatilities of different time resolutions — Analyzing the dynamics of market components (1997) — link
  347. Can we infer microscopic financial information from the long memory in market-order flow?: a quantitative test of the Lillo-Mike-Farmer model (2023) — link
  348. " U ber die von der molekularkinetischen Theorie der W" a rme geforderte Bewegung von in ruhenden Fl" u ssigkeiten suspendierten Teilchen (1905) — link
  349. Stochastic climate models Part I. Theory (1976) — link
  350. Collective Phenomena in Economic Systems (2020) — link
  351. Who Possesses Whom in Terms of the Global Ownership Network (2021) — link
  352. Bitcoin’s Crypto Flow Network (2021) — link
  353. Interdependencies and Causalities in Coupled Financial Networks (2016) — link
  354. Sparse Causality Network Retrieval from Short Time Series (2017) — link
  355. Discrete Hodge Theory on Graphs: A Tutorial (2013) — link
  356. Applications of the Helmholtz-Hodge Decomposition to Networks and Random Processes (2020)
  357. Granger Causality in Multivariate Time Series Using a Time-Ordered Restricted Vector Autoregressive Model (2016) — link
  358. Evaluation of Granger Causality Measures for Constructing Networks from Multivariate Time Series (2019) — link
  359. Estimating the Dimension of a Model (1978) — link
  360. US Research Returns Data. 49 Industry Portfolios [Daily] (2024)
  361. Production of U.S. SMB and HML in the Fama-French Data Library (2023) — link
  362. Industry costs of equity (1997) — link
  363. Industry Classifications and Return Comovement (2007) — link
  364. Hodge Decomposition of Information Flow on Complex Networks (2015) — link
  365. Construction Materials Prices Increase More Than 20 Percent (2022)
  366. Causes and Consequences of the 2023 Banking Crisis (2023) — link
  367. The Global Stock Market Reactions to the 2016 U.S. Presidential Election (2023) — link
  368. Cycling and reciprocity in weighted food webs and economic networks (2021) — link
  369. Hidden interactions in financial markets (2019) — link
  370. Linear and nonlinear causality in financial markets (2023) — link
  371. Financial networks based on Granger causality: A case study (2017) — link
  372. On the Helmholtz Theorem and Its Generalization for Multi-Layers (2016) — link
  373. Characteristics of Principal Components in Stock Price Correlation (2021) — link
  374. Helmholtz-Hodge-Kodaira Decomposition on Financial Data by Ken French (2024)
  375. Too much covariates in a multivariable model may cause the problem of overfitting (2014) — link
  376. What You See May Not Be What You Get: A Brief, Nontechnical Introduction to Overfitting in Regression-Type Models (2004)
  377. Correlations Genuine and Spurious in Pearson and Yule (1995)
  378. A review of the Granger-causality fallacy (2015) — link
  379. A study of problems encountered in Granger causality analysis from a neuroscience perspective (2017) — link
  380. How directed is a directed network? (2020) — link

1 of 388 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.