# Information Flow Rate for Cross-Correlated Stochastic Processes

arXiv: https://arxiv.org/abs/2401.04950 · HTML: https://mlsanity.com/paper/2401.04950/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 85 references that are in the map.
- First posted on arXiv 10 Jan 2024.

## Builds on (most cited first, 7 of 7)

- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [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)
- [Multivariate Gaussian and Student-t Process Regression for Multi-output Prediction](https://mlsanity.com/paper/1703.04455/) (2017)
- [Cross-Covariance Functions for Multivariate Geostatistics](https://mlsanity.com/paper/1507.08017/) (2015)
- [Granger Causality in Multi-variate Time Series using a Time Ordered Restricted Vector Autoregressive Model](https://mlsanity.com/paper/1511.03463/) (2015)
- [Normalized multivariate time series causality analysis and causal graph reconstruction](https://mlsanity.com/paper/2104.11360/) (2021)
- [Non-separable Covariance Kernels for Spatiotemporal Gaussian Processes based on a Hybrid Spectral Method and the Harmonic Oscillator](https://mlsanity.com/paper/2302.09580/) (2023)

## Built on by (most cited first, 1 of 1)

- [Wavelet Mixture of Experts for Time Series Forecasting](https://mlsanity.com/paper/2508.08825/) (2025)

## Abstract (arXiv)

Causal inference seeks to identify cause-and-effect interactions in coupled systems. A recently proposed method by Liang detects causal relations by quantifying the direction and magnitude of information flow between time series. The theoretical formulation of information flow for stochastic dynamical systems provides a general expression and a data-driven statistic for the rate of entropy transfer between different system units. To advance understanding of information flow rate in terms of intuitive concepts and physically meaningful parameters, we investigate statistical properties of the data-driven information flow rate between coupled stochastic processes. We derive relations between the expectation of the information flow rate statistic and properties of the auto- and cross-correlation functions. Thus, we elucidate the dependence of the information flow rate on the analytical properties and characteristic times of the correlation functions. Our analysis provides insight into the influence of the sampling step, the strength of cross-correlations, and the temporal delay of correlations on information flow rate. We support the theoretical results with numerical simulations of correlated Gaussian processes.