Analyzing Multiple Nonlinear Time Series with Extended Granger Causality

Identifying causal relations among simultaneously acquired signals is an important problem in multivariate time series analysis. For linear stochastic systems Granger proposed a simple procedure called the Granger causality to detect such relations. In this work we consider nonlinear extensions of Granger's idea and refer to the result as Extended Granger Causality. A simple approach implementing the Extended Granger Causality is presented and applied to multiple chaotic time series and other types of nonlinear signals. In addition, for situations with three or more time series we propose a conditional Extended Granger Causality measure that enables us to determine whether the causal relation between two signals is direct or mediated by another process.Comment: 16 pages, 6 figure

Detection of Change--Points in the Spectral Density. With Applications to ECG Data

We propose a new method for estimating the change-points of heart rate in the orthosympathetic and parasympathetic bands, based on the wavelet transform in the complex domain and the study of the change-points in the moments of the modulus of these wavelet transforms. We observe change-points in the distribution for both bands.Comment: proceeding of the workshop 'Fouille de donn\'ees temporelles et analyse de flux de donn\'ees' EGC'2009, january 27, Strasbourg, Franc

Granger Causality and the Sampling of Economic Processes

This paper provides a discussion of the developments in econometric modelling that are designed to deal with the problem of spurious Granger causality relationships that can arise from temporal aggregation.We outline the distortional e ects of using discrete time models that explicitly depend on the unit of time and outline a remedy of constructing timeinvariant discrete time models via a structural continuous time model.In an application to testing for money-income causality, we demonstrate the importance of incorporating exact temporal aggregation restrictions on the discrete time data.We do this by conducting causality tests in discrete time models that: (a) impose the temporal aggregation restrictions exactly; (b) impose the temporal aggregation restrictions approximately; and (c) do not impose these restrictions at all.sampling;aggregation;models

Bits from Biology for Computational Intelligence

Computational intelligence is broadly defined as biologically-inspired computing. Usually, inspiration is drawn from neural systems. This article shows how to analyze neural systems using information theory to obtain constraints that help identify the algorithms run by such systems and the information they represent. Algorithms and representations identified information-theoretically may then guide the design of biologically inspired computing systems (BICS). The material covered includes the necessary introduction to information theory and the estimation of information theoretic quantities from neural data. We then show how to analyze the information encoded in a system about its environment, and also discuss recent methodological developments on the question of how much information each agent carries about the environment either uniquely, or redundantly or synergistically together with others. Last, we introduce the framework of local information dynamics, where information processing is decomposed into component processes of information storage, transfer, and modification -- locally in space and time. We close by discussing example applications of these measures to neural data and other complex systems