Inferring causality in networks of WSS processes by pairwise estimation methods

Inferring causal dependences in a family of dynamic systems from a finite set of observations is a problem encountered in many applications that arise in a diverse variety of fields; ranging from economics and finance to climatology and neuroscience. Given a set of random processes, the objective is to determine whether one process is influenced by the others and to investigate the nature of this influence in case a dependence relation is identified. The notion of Granger-causality may be used in this context to measure and quantify causal structures. Ideally, in order to infer the complete interdependence structure of a complex system, one should simultaneously consider the dynamic behaviour of all the processes involved. However, for large networks, such a method becomes exceedingly complicated. In this paper, we consider an interdependent group of jointly wide sense stationary real-valued stochastic processes and investigate the problem of determining Granger-causality by identifying pairwise causal relations. It is seen that while such methods may not reveal all details of a system, they can nonetheless provide useful and reasonably accurate information.

[1]  M. Shams,et al.  Money-velocity causality detection : Evidence from some developing countries , 1989 .

[2]  C. Granger.  Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[3]  Todd P. Coleman,et al.  Estimating the directed information to infer causal relationships in ensemble neural spike train recordings , 2010, Journal of Computational Neuroscience.

[4]  J. Massey.  CAUSALITY, FEEDBACK AND DIRECTED INFORMATION , 1990 .

[5]  Clive W. J. Granger,et al.  Some recent developments in a concept of causality , 2001 .

[6]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[7]  Donatello Materassi,et al.  Topological identification in networks of dynamical systems , 2008, 2008 47th IEEE Conference on Decision and Control.

[8]  C. Granger.  Testing for causality: a personal viewpoint , 1980 .

[9]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[10]  Haim H. Permuter,et al.  Universal Estimation of Directed Information , 2010, IEEE Transactions on Information Theory.

[11]  Haim H. Permuter,et al.  Directed Information, Causal Estimation, and Communication in Continuous Time , 2009, IEEE Transactions on Information Theory.

[12]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[13]  T. Sauer,et al.  Reconstructing the topology of sparsely connected dynamical networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  H. Marko,et al.  The Bidirectional Communication Theory - A Generalization of Information Theory , 1973, IEEE Transactions on Communications.

[15]  Ian Stewart,et al.  Networking opportunity , 2004, Nature.

[16]  C. Granger.  Some recent development in a concept of causality , 1988 .

[17]  T. Schreiber,et al.  Information transfer in continuous processes , 2002 .

[18]  Schreiber,et al.  Measuring information transfer , 2000, Physical review letters.

[19]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[20]  Olivier J. J. Michel,et al.  On directed information theory and Granger causality graphs , 2010, Journal of Computational Neuroscience.

[21]  Olivier J. J. Michel,et al.  Relating Granger causality to directed information theory for networks of stochastic processes , 2009, 0911.2873.

[22]  C. Sims.  Money, Income, and Causality , 1972 .

[23]  Marc Timme,et al.  Revealing network connectivity from response dynamics. , 2006, Physical review letters.

[24]  Haim H. Permuter,et al.  Interpretations of Directed Information in Portfolio Theory, Data Compression, and Hypothesis Testing , 2009, IEEE Transactions on Information Theory.

[25]  Murti V. Salapaka,et al.  On the Problem of Reconstructing an Unknown Topology via Locality Properties of the Wiener Filter , 2010, IEEE Transactions on Automatic Control.