# Granger Causality: A Review and Recent Advances

arXiv: https://arxiv.org/abs/2105.02675 · HTML: https://mlsanity.com/paper/2105.02675/

## Key facts

- Cited by 63 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 135 references that are in the map.
- First posted on arXiv 5 May 2021.

## Builds on (most cited first, 21 of 21)

- [Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1801.01236/) (2018)
- [Learning Granger Causality for Hawkes Processes](https://mlsanity.com/paper/1602.04511/) (2016)
- [Diffusion Convolutional Recurrent Neural Network: Data-Driven Traffic Forecasting](https://mlsanity.com/paper/1707.01926/) (2017)
- [Regularized estimation in sparse high-dimensional time series models](https://mlsanity.com/paper/1311.4175/) (2013)
- [Long-term Forecasting using Higher Order Tensor RNNs](https://mlsanity.com/paper/1711.00073/) (2017)
- [Neural Granger Causality](https://mlsanity.com/paper/1802.05842/) (2018)
- [In reply to Faes et al. and Barnett et al. regarding "A study of problems encountered in Granger causality analysis from a neuroscience perspective"](https://mlsanity.com/paper/1709.10248/) (2017)
- [Causal Discovery from Subsampled Time Series Data by Constraint Optimization](https://mlsanity.com/paper/1602.07970/) (2016)
- [Low Rank and Structured Modeling of High-dimensional Vector Autoregressions](https://mlsanity.com/paper/1812.03568/) (2018)
- [Network Reconstruction From High Dimensional Ordinary Differential Equations](https://mlsanity.com/paper/1610.03177/) (2016)
- [The Multivariate Hawkes Process in High Dimensions: Beyond Mutual Excitation](https://mlsanity.com/paper/1707.04928/) (2017)
- [Joint Structural Break Detection and Parameter Estimation in High-Dimensional Non-Stationary VAR Models](https://mlsanity.com/paper/1711.07357/) (2017)
- [Identifiability and Estimation of Structural Vector Autoregressive Models for Subsampled and Mixed Frequency Time Series](https://mlsanity.com/paper/1704.02519/) (2017)
- [A Unified Theory of Confidence Regions and Testing for High Dimensional Estimating Equations](https://mlsanity.com/paper/1510.08986/) (2015)
- [Statistical Inference for Networks of High-Dimensional Point Processes](https://mlsanity.com/paper/2007.07448/) (2020)
- [Inference of High-dimensional Autoregressive Generalized Linear Models](https://mlsanity.com/paper/1605.02693/) (2016)
- [Bayesian nonparametric sparse VAR models](https://mlsanity.com/paper/1608.02740/) (2016)
- [Hierarchical Attention-Based Recurrent Highway Networks for Time Series Prediction](https://mlsanity.com/paper/1806.00685/) (2018)
- [Spatio-Temporal Low Count Processes with Application to Violent Crime Events](https://mlsanity.com/paper/1304.5642/) (2013)
- [Testing for high-dimensional network parameters in auto-regressive models](https://mlsanity.com/paper/1812.03659/) (2018)
- [Confidence intervals for parameters in high-dimensional sparse vector autoregression](https://mlsanity.com/paper/2009.09462/) (2020)

## Built on by (most cited first, 30 of 63)

- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [The Essential Role of Causality in Foundation World Models for Embodied AI](https://mlsanity.com/paper/2402.06665/) (2024)
- [MECD: Unlocking Multi-Event Causal Discovery in Video Reasoning](https://mlsanity.com/paper/2409.17647/) (2024)
- [Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes](https://mlsanity.com/paper/2402.18477/) (2024)
- [CausalFormer: An Interpretable Transformer for Temporal Causal Discovery](https://mlsanity.com/paper/2406.16708/) (2024)
- [Interpretation of Time-Series Deep Models: A Survey](https://mlsanity.com/paper/2305.14582/) (2023)
- [DIGRAC: Digraph Clustering Based on Flow Imbalance](https://mlsanity.com/paper/2106.05194/) (2021)
- [STGC-GNNs: A GNN-based traffic prediction framework with a spatial-temporal Granger causality graph](https://mlsanity.com/paper/2210.16789/) (2022)
- [Lead-lag detection and network clustering for multivariate time series with an application to the US equity market](https://mlsanity.com/paper/2201.08283/) (2022)
- [Granger causal inference on DAGs identifies genomic loci regulating transcription](https://mlsanity.com/paper/2210.10168/) (2022)
- [CEBoosting: Online Sparse Identification of Dynamical Systems with Regime Switching by Causation Entropy Boosting](https://mlsanity.com/paper/2304.07863/) (2023)
- [Learning Granger Causality from Instance-wise Self-attentive Hawkes Processes](https://mlsanity.com/paper/2402.03726/) (2024)
- [Granger Causal Chain Discovery for Sepsis-Associated Derangements via Continuous-Time Hawkes Processes](https://mlsanity.com/paper/2209.04480/) (2022)
- [Causal inference in drug discovery and development](https://mlsanity.com/paper/2209.14664/) (2022)
- [Causal Inference for Banking Finance and Insurance A Survey](https://mlsanity.com/paper/2307.16427/) (2023)
- [CausalMMM: Learning Causal Structure for Marketing Mix Modeling](https://mlsanity.com/paper/2406.16728/) (2024)
- [MECD+: Unlocking Event-Level Causal Graph Discovery for Video Reasoning](https://mlsanity.com/paper/2501.07227/) (2025)
- [Double Machine Learning Based Structure Identification from Temporal Data](https://mlsanity.com/paper/2311.06012/) (2023)
- [TFT-multi: simultaneous forecasting of vital sign trajectories in the ICU](https://mlsanity.com/paper/2409.15586/) (2024)
- [ELATE: Evolutionary Language model for Automated Time-series Engineering](https://mlsanity.com/paper/2508.14667/) (2025)
- [Feature Selection for Fault Detection and Prediction based on Event Log Analysis](https://mlsanity.com/paper/2208.09440/) (2022)
- [TNPAR: Topological Neural Poisson Auto-Regressive Model for Learning Granger Causal Structure from Event Sequences](https://mlsanity.com/paper/2306.14114/) (2023)
- [Agentic Personalisation of Cross-Channel Marketing Experiences](https://mlsanity.com/paper/2506.16429/) (2025)
- [Bayesian Vector AutoRegression with Factorised Granger-Causal Graphs](https://mlsanity.com/paper/2402.03614/) (2024)
- [STARFormer: A Novel Spatio-Temporal Aggregation Reorganization Transformer of FMRI for Brain Disorder Diagnosis](https://mlsanity.com/paper/2501.00378/) (2024)
- [Domain-Adapted Granger Causality for Real-Time Cross-Slice Attack Attribution in 6G Networks](https://mlsanity.com/paper/2510.05165/) (2025)
- [UnCLe: Towards Scalable Dynamic Causal Discovery in Non-linear Temporal Systems](https://mlsanity.com/paper/2511.03168/) (2025)
- [Causal Discovery in High-Dimensional Point Process Networks with Hidden Nodes](https://mlsanity.com/paper/2109.10947/) (2021)
- [Information Theoretic Measures of Causal Influences during Transient Neural Events](https://mlsanity.com/paper/2209.07508/) (2022)
- [Causal Graph Discovery from Self and Mutually Exciting Time Series](https://mlsanity.com/paper/2301.11197/) (2023)

## Abstract (arXiv)

Introduced more than a half century ago, Granger causality has become a popular tool for analyzing time series data in many application domains, from economics and finance to genomics and neuroscience. Despite this popularity, the validity of this notion for inferring causal relationships among time series has remained the topic of continuous debate. Moreover, while the original definition was general, limitations in computational tools have primarily limited the applications of Granger causality to simple bivariate vector auto-regressive processes or pairwise relationships among a set of variables. Starting with a review of early developments and debates, this paper discusses recent advances that address various shortcomings of the earlier approaches, from models for high-dimensional time series to more recent developments that account for nonlinear and non-Gaussian observations and allow for sub-sampled and mixed frequency time series.