Stationary Processes, Wiener-Granger Causality, and Matrix Spectral Factorization
Granger causality has become an indispensable tool for analyzing causal relationships between time series. In this paper, we provide a detailed overview of its mathematical foundations, trace its historical development, and explore how recent computational advancements can enhance its application in various fields. We will not hesitate to present the proofs in full if they are simple and transparent. For more complex theorems on which we rely, we will provide supporting citations. We also discuss potential future directions for the method, particularly in the context of largescale data analysis.
Code (0)
등록된 구현이 없습니다.
Tasks
Time SeriesSimilar Papers 제목 키워드 기반
Granger Causality from Quantized Measurements
An approach is proposed for inferring Granger causality between jointly stationary, Gaussian signals from quantized data. First, a necessary and sufficient rank criterion for the equality of two conditional Gaussian dist…
Gaussian ProcessesQuantizationRobust Non-linear Wiener-Granger Causality For Large High-dimensional Data
Wiener-Granger causality is a widely used framework of causal analysis for temporally resolved events. We introduce a new measure of Wiener-Granger causality based on kernelization of partial canonical correlation analys…
Vocal Bursts Intensity PredictionNon-linear dependence and Granger causality: A vine copula approach
Inspired by Jang et al. (2022), we propose a Granger causality-in-the-mean test for bivariate $k-$Markov stationary processes based on a recently introduced class of non-linear models, i.e., vine copula models. By means …
Jacobian Granger Causal Neural Networks for Analysis of Stationary and Nonstationary Data
Granger causality is a commonly used method for uncovering information flow and dependencies in a time series. Here we introduce JGC (Jacobian Granger Causality), a neural network-based approach to Granger causality usin…
Time SeriesTime Series AnalysisPrediction and Causality of functional MRI and synthetic signal using a Zero-Shot Time-Series Foundation Model
Time-series forecasting and causal discovery are central in neuroscience, as predicting brain activity and identifying causal relationships between neural populations and circuits can shed light on the mechanisms underly…