Related papers: Non-linear dependence and Granger causality: A vin…
A widely applied approach to causal inference from a non-experimental time series $X$, often referred to as "(linear) Granger causal analysis", is to regress present on past and interpret the regression matrix $\hat{B}$ causally. However,…
Wahl et al. (2016, 2017) introduced the idea of Granger causality (GC) maps for Langevin systems: dynamics are localised linearly at each point in phase space as vector Ornstein-Uhlenbeck (VOU) processes, for which GCs may in principle be…
Vine copulas are a type of multivariate dependence model, composed of a collection of bivariate copulas that are combined according to a specific underlying graphical structure. Their flexibility and practicality in moderate and high…
Quantile regression is a field with steadily growing importance in statistical modeling. It is a complementary method to linear regression, since computing a range of conditional quantile functions provides a more accurate modelling of the…
We propose stepwise variational inference (VI) with vine copulas: a universal VI procedure that combines vine copulas with a novel stepwise estimation procedure of the variational parameters. Vine copulas consist of a nested sequence of…
In this paper we test for Granger causality in high-dimensional vector autoregressive models (VARs) to disentangle and interpret the complex causal chains linking radiative forcings and global temperatures. By allowing for high…
The relationship between statistical dependency and causality lies at the heart of all statistical approaches to causal inference. Recent results in the ChaLearn cause-effect pair challenge have shown that causal directionality can be…
We define a copula process which describes the dependencies between arbitrarily many random variables independently of their marginal distributions. As an example, we develop a stochastic volatility model, Gaussian Copula Process Volatility…
It is often useful in multivariate time series analysis to determine statistical causal relations between different time series. Granger causality is a fundamental measure for this purpose. Yet the traditional pairwise approach to Granger…
Weakly stationary Gaussian processes (GPs) are the principal tool in the statistical approaches to the design and analysis of computer experiments (or Uncertainty Quantification). Such processes are fitted to computer model output using a…
Calculating the degree of non-Markovianity of a dissipative process is a difficult task, even for the dynamics of a single qubit, given the complex maximization problem. In this work, focusing on the entanglement-based quantifier of…
In many practical scenarios, including finance, environmental sciences, system reliability, etc., it is often of interest to study the various notion of negative dependence among the observed variables. A new bivariate copula is proposed…
We study Ising models for describing data and show that autoregressive methods may be used to learn their connections, also in the case of asymmetric connections and for multi-spin interactions. For each link the linear Granger causality is…
Vine copulas are a useful statistical tool to describe the dependence structure between several random variables, especially when the number of variables is very large. When modeling data with vine copulas, one often is confronted with a…
A two-component model for the evolution of real GDP per capita in the USA is presented and tested. The first component of the GDP growth rate represents an economic trend and is inversely proportional to the attained level of real GDP per…
When a dynamical system can be modeled as a sequence of observations, Granger causality is a powerful approach for detecting predictive interactions between its variables. However, traditional Granger causal inference has limited utility in…
We consider the Granger causal structure learning problem from time series data. Granger causal algorithms predict a 'Granger causal effect' between two variables by testing if prediction error of one decreases significantly in the absence…
A dependence measure for arbitrary type pairs of random variables is proposed and analyzed, which in the particular case where both random variables are continuous turns out to be a concordance measure. Also, a sample version of the…
Linear regression model (LRM) based on mean square error (MSE) criterion is widely used in Granger causality analysis (GCA), which is the most commonly used method to detect the causality between a pair of time series. However, when signals…
The paper presents a new copula based method for measuring dependence between random variables. Our approach extends the Maximum Mean Discrepancy to the copula of the joint distribution. We prove that this approach has several advantageous…