Related papers: Statistical Inference for Local Granger Causality
We propose a new measure to estimate the direction of information flux in multivariate time series from complex systems. This measure, based on the slope of the phase spectrum (Phase Slope Index) has invariance properties that are important…
In this paper, we study a notion of local stationarity for discrete time Markov chains which is useful for applications in statistics. In the spirit of some locally stationary processes introduced in the literature, we consider triangular…
This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of…
Our goal is to estimate causal interactions in multivariate time series. Using vector autoregressive (VAR) models, these can be defined based on non-vanishing coefficients belonging to respective time-lagged instances. As in most cases a…
Causality analysis is an important problem lying at the heart of science, and is of particular importance in data science and machine learning. An endeavor during the past 16 years viewing causality as real physical notion so as to…
We propose a graphical model for representing networks of stochastic processes, the minimal generative model graph. It is based on reduced factorizations of the joint distribution over time. We show that under appropriate conditions, it is…
This paper considers joint learning of multiple sparse Granger graphical models to discover underlying common and differential Granger causality (GC) structures across multiple time series. This can be applied to drawing group-level brain…
Transfer entropy, an information-theoretic measure of time-directed information transfer between joint processes, has steadily gained popularity in the analysis of complex stochastic dynamics in diverse fields, including the neurosciences,…
We develop an LM test for Granger causality in high-dimensional VAR models based on penalized least squares estimations. To obtain a test retaining the appropriate size after the variable selection done by the lasso, we propose a…
The article contains an overview over locally stationary processes. At the beginning time varying autoregressive processes are discussed in detail - both as as a deep example and an important class of locally stationary processes. In the…
Classical causal models, such as Granger causality and structural equation modeling, are largely restricted to acyclic interactions and struggle to represent cyclic and higher-order dynamics in complex networks. We introduce a causal…
At least two recent developments have put the spotlight on some significant gaps in the theory of multivariate time series. The recent interest in the dynamics of networks; and the advent, across a range of applications, of measuring…
We propose the Granger causality inference Kolmogorov-Arnold Networks (KANGCI), a novel architecture that extends the recently proposed Kolmogorov-Arnold Networks (KAN) to the domain of causal inference. By extracting base weights from KAN…
Trivariate Granger causality analysis seeks to distinguish between "true" causality and "spurious" causality results from the topology of the system. However, this analysis is sensitive both to the choice of test criteria and the presence…
Locally stationary Hawkes processes have been introduced in order to generalise classical Hawkes processes away from stationarity by allowing for a time-varying second-order structure. This class of self-exciting point processes has…
The scientific rigor and computational methods of causal inference have had great impacts on many disciplines, but have only recently begun to take hold in spatial applications. Spatial casual inference poses analytic challenges due to…
This paper considers a time-varying vector error-correction model that allows for different time series behaviours (e.g., unit-root and locally stationary processes) to interact with each other to co-exist. From practical perspectives, this…
We analyze a neural system which mimics a sensorial cortex, with different input characteristics, in presence of transmission delays. We propose a new measure to characterize collective behavior, based on the nonlinear extension of the…
The intention of this paper is to discuss the mathematical model of causality introduced by C.W.J. Granger in 1969. The Granger's model of causality has become well-known and often used in various econometric models describing causal…
We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to…