Granger Causality

Order-Constrained Spectral Causality in Multivariate Time Series ArXiv ID: 2601.01216 “View on arXiv” Authors: Alejandro Rodriguez Dominguez Abstract We introduce an operator-theoretic framework for causal analysis in multivariate time series based on order-constrained spectral non-invariance. Directional influence is defined as sensitivity of second-order dependence operators to admissible, order-preserving temporal deformations of a designated source component, yielding an intrinsically multivariate causal notion summarized through orthogonally invariant spectral functionals. Under linear Gaussian assumptions, the criterion coincides with linear Granger causality, while beyond this regime it captures collective and nonlinear directional dependence not reflected in pairwise predictability. We establish existence, uniform consistency, and valid inference for the resulting non-smooth supremum–infimum statistics using shift-based randomization that exploits order-induced group invariance, yielding finite-sample exactness under exact invariance and asymptotic validity under weak dependence without parametric assumptions. Simulations demonstrate correct size and strong power against distributed and bulk-dominated alternatives, including nonlinear dependence missed by linear Granger tests with appropriate feature embeddings. An empirical application to a high-dimensional panel of daily financial return series spanning major asset classes illustrates system-level causal monitoring in practice. Directional organization is episodic and stress-dependent, causal propagation strengthens while remaining multi-channel, dominant causal hubs reallocate rapidly, and statistically robust transmission channels are sparse and horizon-heterogeneous even when aggregate lead–lag asymmetry is weak. The framework provides a scalable and interpretable complement to correlation-, factor-, and pairwise Granger-style analyses for complex systems. ...

From News to Returns: A Granger-Causal Hypergraph Transformer on the Sphere ArXiv ID: 2510.04357 “View on arXiv” Authors: Anoushka Harit, Zhongtian Sun, Jongmin Yu Abstract We propose the Causal Sphere Hypergraph Transformer (CSHT), a novel architecture for interpretable financial time-series forecasting that unifies \emph{“Granger-causal hypergraph structure”}, \emph{“Riemannian geometry”}, and \emph{“causally masked Transformer attention”}. CSHT models the directional influence of financial news and sentiment on asset returns by extracting multivariate Granger-causal dependencies, which are encoded as directional hyperedges on the surface of a hypersphere. Attention is constrained via angular masks that preserve both temporal directionality and geometric consistency. Evaluated on S&P 500 data from 2018 to 2023, including the 2020 COVID-19 shock, CSHT consistently outperforms baselines across return prediction, regime classification, and top-asset ranking tasks. By enforcing predictive causal structure and embedding variables in a Riemannian manifold, CSHT delivers both \emph{“robust generalisation across market regimes”} and \emph{“transparent attribution pathways”} from macroeconomic events to stock-level responses. These results suggest that CSHT is a principled and practical solution for trustworthy financial forecasting under uncertainty. ...

Investor Sentiment and Market Movements: A Granger Causality Perspective ArXiv ID: 2510.15915 “View on arXiv” Authors: Tamoghna Mukherjee Abstract The stock market is heavily influenced by investor sentiment, which can drive buying or selling behavior. Sentiment analysis helps in gauging the overall sentiment of market participants towards a particular stock or the market as a whole. Positive sentiment often leads to increased buying activity and vice versa. Granger causality can be applied to ascertain whether changes in sentiment precede changes in stock prices.The study is focused on this aspect and tries to understand the relationship between close price index and sentiment score with the help of Granger causality inference. The study finds a positive response through hypothesis testing. ...

Non-parametric Causal Discovery for EU Allowances Returns Through the Information Imbalance ArXiv ID: 2508.15667 “View on arXiv” Authors: Cristiano Salvagnin, Vittorio del Tatto, Maria Elena De Giuli, Antonietta Mira, Aldo Glielmo Abstract We propose to use a recently introduced non-parametric tool named Differentiable Information Imbalance (DII) to identify variables that are causally related – potentially through non-linear relationships – to the financial returns of the European Union Allowances (EUAs) within the EU Emissions Trading System (EU ETS). We examine data from January 2013 to April 2024 and compare the DII approach with multivariate Granger causality, a well-known linear approach based on VAR models. We find significant overlap among the causal variables identified by linear and non-linear methods, such as the coal futures prices and the IBEX35 index. We also find important differences between the two causal sets identified. On two synthetic datasets, we show how these differences could originate from limitations of the linear methodology. ...

A Framework for Predictive Directional Trading Based on Volatility and Causal Inference ArXiv ID: 2507.09347 “View on arXiv” Authors: Ivan Letteri Abstract Purpose: This study introduces a novel framework for identifying and exploiting predictive lead-lag relationships in financial markets. We propose an integrated approach that combines advanced statistical methodologies with machine learning models to enhance the identification and exploitation of predictive relationships between equities. Methods: We employed a Gaussian Mixture Model (GMM) to cluster nine prominent stocks based on their mid-range historical volatility profiles over a three-year period. From the resulting clusters, we constructed a multi-stage causal inference pipeline, incorporating the Granger Causality Test (GCT), a customised Peter-Clark Momentary Conditional Independence (PCMCI) test, and Effective Transfer Entropy (ETE) to identify robust, predictive linkages. Subsequently, Dynamic Time Warping (DTW) and a K-Nearest Neighbours (KNN) classifier were utilised to determine the optimal time lag for trade execution. The resulting strategy was rigorously backtested. Results: The proposed volatility-based trading strategy, tested from 8 June 2023 to 12 August 2023, demonstrated substantial efficacy. The portfolio yielded a total return of 15.38%, significantly outperforming the 10.39% return of a comparative Buy-and-Hold strategy. Key performance metrics, including a Sharpe Ratio up to 2.17 and a win rate up to 100% for certain pairs, confirmed the strategy’s viability. Conclusion: This research contributes a systematic and robust methodology for identifying profitable trading opportunities derived from volatility-based causal relationships. The findings have significant implications for both academic research in financial modelling and the practical application of algorithmic trading, offering a structured approach to developing resilient, data-driven strategies. ...

Detecting Fraud in Financial Networks: A Semi-Supervised GNN Approach with Granger-Causal Explanations ArXiv ID: 2507.01980 “View on arXiv” Authors: Linh Nguyen, Marcel Boersma, Erman Acar Abstract Fraudulent activity in the financial industry costs billions annually. Detecting fraud, therefore, is an essential yet technically challenging task that requires carefully analyzing large volumes of data. While machine learning (ML) approaches seem like a viable solution, applying them successfully is not so easy due to two main challenges: (1) the sparsely labeled data, which makes the training of such approaches challenging (with inherent labeling costs), and (2) lack of explainability for the flagged items posed by the opacity of ML models, that is often required by business regulations. This article proposes SAGE-FIN, a semi-supervised graph neural network (GNN) based approach with Granger causal explanations for Financial Interaction Networks. SAGE-FIN learns to flag fraudulent items based on weakly labeled (or unlabelled) data points. To adhere to regulatory requirements, the flagged items are explained by highlighting related items in the network using Granger causality. We empirically validate the favorable performance of SAGE-FIN on a real-world dataset, Bipartite Edge-And-Node Attributed financial network (Elliptic++), with Granger-causal explanations for the identified fraudulent items without any prior assumption on the network structure. ...

From Data Acquisition to Lag Modeling: Quantitative Exploration of A-Share Market with Low-Coupling System Design ArXiv ID: 2506.19255 “View on arXiv” Authors: Jianyong Fang, Sitong Wu, Junfan Tong Abstract We propose a novel two-stage framework to detect lead-lag relationships in the Chinese A-share market. First, long-term coupling between stocks is measured via daily data using correlation, dynamic time warping, and rank-based metrics. Then, high-frequency data (1-, 5-, and 15-minute) is used to detect statistically significant lead-lag patterns via cross-correlation, Granger causality, and regression models. Our low-coupling modular system supports scalable data processing and improves reproducibility. Results show that strongly coupled stock pairs often exhibit lead-lag effects, especially at finer time scales. These findings provide insights into market microstructure and quantitative trading opportunities. ...

Multiscale Causal Analysis of Market Efficiency via News Uncertainty Networks and the Financial Chaos Index ArXiv ID: 2505.01543 “View on arXiv” Authors: Masoud Ataei Abstract This study evaluates the scale-dependent informational efficiency of stock markets using the Financial Chaos Index, a tensor-eigenvalue-based measure of realized volatility. Incorporating Granger causality and network-theoretic analysis across a range of economic, policy, and news-based uncertainty indices, we assess whether public information is efficiently incorporated into asset price fluctuations. Based on a 34-year time period from 1990 to 2023, at the daily frequency, the semi-strong form of the Efficient Market Hypothesis is rejected at the 1% level of significance, indicating that asset price changes respond predictably to lagged news-based uncertainty. In contrast, at the monthly frequency, such predictive structure largely vanishes, supporting informational efficiency at coarser temporal resolutions. A structural analysis of the Granger causality network reveals that fiscal and monetary policy uncertainties act as core initiators of systemic volatility, while peripheral indices, such as those related to healthcare and consumer prices, serve as latent bridges that become activated under crisis conditions. These findings underscore the role of time-scale decomposition and structural asymmetries in diagnosing market inefficiencies and mapping the propagation of macro-financial uncertainty. ...

Causality Analysis of COVID-19 Induced Crashes in Stock and Commodity Markets: A Topological Perspective ArXiv ID: 2502.14431 “View on arXiv” Authors: Unknown Abstract The paper presents a comprehensive causality analysis of the US stock and commodity markets during the COVID-19 crash. The dynamics of different sectors are also compared. We use Topological Data Analysis (TDA) on multidimensional time-series to identify crashes in stock and commodity markets. The Wasserstein Distance WD shows distinct spikes signaling the crash for both stock and commodity markets. We then compare the persistence diagrams of stock and commodity markets using the WD metric. A significant spike in the $WD$ between stock and commodity markets is observed during the crisis, suggesting significant topological differences between the markets. Similar spikes are observed between the sectors of the US market as well. Spikes obtained may be due to either a difference in the magnitude of crashes in the two markets (or sectors), or from the temporal lag between the two markets suggesting information flow. We study the Granger-causality between stock and commodity markets and also between different sectors. The results show a bidirectional Granger-causality between commodity and stock during the crash period, demonstrating the greater interdependence of financial markets during the crash. However, the overall analysis shows that the causal direction is from stock to commodity. A pairwise Granger-causal analysis between US sectors is also conducted. There is a significant increase in the interdependence between the sectors during the crash period. TDA combined with Granger-causality effectively analyzes the interdependence and sensitivity of different markets and sectors. ...

An Analysis of the Interdependence Between Peanut and Other Agricultural Commodities in China’s Futures Market ArXiv ID: 2501.16697 “View on arXiv” Authors: Unknown Abstract This study analyzes historical data from five agricultural commodities in the Chinese futures market to explore the correlation, cointegration, and Granger causality between Peanut futures and related futures. Multivariate linear regression models are constructed for prices and logarithmic returns, while dynamic relationships are examined using VAR and DCC-EGARCH models. The results reveal a significant dynamic linkage between Peanut and Soybean Oil futures through DCC-EGARCH, whereas the VAR model suggests limited influence from other futures. Additionally, the application of MLP, CNN, and LSTM neural networks for price prediction highlights the critical role of time step configurations in forecasting accuracy. These findings provide valuable insights into the interconnectedness of agricultural futures markets and the efficacy of advanced modeling techniques in financial analysis. ...