Phase Synchronization and Cointegration: Bridging Two Theories
Rainer Dahlhaus (Universitaet Heidelberg)



The theory of cointegration has been the leading theory in econometrics with powerful applications to macroeconomics during the last decades. On the other hand phase synchronization for oscillators has been a major research topic in physics for some 15 years with many applications in different areas of science. In particular in neuroscience the understanding of phase synchronization is of importance since phase synchronization is regarded as essential for functional coupling of different brain regions. In an abstract sense both theories describe the dynamic fluctuation around some equilibrium. In this talk we point out that, after some mathematical transformation,  there exists a close connection between both subjects. As a consequence several techniques on statistical inference for cointegrated systems can immediately be applied for statistical inference on phase synchronization based on empirical data. This includes tests for phase synchronization, tests for unidirectional coupling and the identification of the equilibrium from data including phase shifts. We give an example where a chaotic Rössler-Lorenz system is identified with the methods from cointegration. Cointegration may also be used to investigate phase synchronization in complex networks. We also discuss some open problems and the research subject as a whole at the edge between econometrics, statistics, physics and neuroscience.