Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2012-01-03
Nonlinear Sciences
Adaptation and Self-Organizing Systems
Scientific paper
The theory of cointegration has been the leading theory in econometrics with powerful applications to macroeconomics during the last decades. On the other hand the theory of phase synchronization for weakly coupled complex oscillators has been one of the leading theories in physics for some 15 years with many applications to different areas of science. For example in neuroscience 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 paper we point out that there exists a very close connection between both theories. We show that there exists a system of stochastic difference equations which can be viewed as close to the Kuramoto equations, whose solution is a cointegrated system. As one consequence the rich theory 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 an unidirectionally coupled Roessler-Lorenz system is identified with the methods from cointegration. The methods from cointegration may also be used to investigate phase synchronization in complex networks. On the contrary there are many interesting results on phase synchronization which may inspire new research on cointegration.
Dahlhaus Rainer
Neddermeyer Jan C.
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