CHAOS2010 Conference Rendering Statistical Significance of Information Flow Measures Angeliki Papana and Dimitris Kugiumtzis Aristotle University of Thessaloniki Department of Mathematical, Physical and Computational Sciences Faculty of Engineering 54124 Thessaloniki, Greece e-mail: agpapana@gen.auth.gr, dkugiu@gen.auth.gr Abstract. Information causality measures, i.e. transfer entropy and symbolic transfer entropy, are modified using the concept of surrogate data in order to identify correctly the presence and direction of causal effects. The measures are evaluated on multiple bivariate time series of known coupled systems of varying complexity and on a range of embedding dimensions. The proposed modifications of the causality measures are found to reduce the bias in the estimation of the measures and preserve the zero level in the absence of coupling. Keywords: Information flow, Causality, Transfer entropy. 1 Introduction Given a set of time series observations, it is essential to assess whether they originate from coupled or uncoupled systems, detect the hidden causal de- pendencies between them and understand which system is the driver. For these purposes, many model-free measures have been developed based on phase synchronization [8], geometry in state space [1,7] and information the- ory [9,11,10]. There have been recently comparative studies on the different causality measures [2,5]. In a recent evaluation of different causality measures [6], we observed in many cases significant measure values in the absence of coupling that can be misinterpreted as weak coupling. Here, we investigate this on information measures. Their estimation involves the estimation of entropies that can have bias depending on the time series length, state space recon- struction and system complexity. We attempt to establish the zero level of information measures when the systems are not coupled and for this we use surrogate data. The suggested surrogates are extracted by randomly shuffling the reconstructed points of the driving time series, so that the dynamical properties of each system are preserved in the point representation and only the coupling, if present, is de- stroyed. We believe that shuffling randomly the reconstructed points is more appropriate than shuffling the samples of the driving time series, as proposed