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On the Relationship Between the Theory of Cointegration and the Theory of Phase Synchronization by Dahlhaus, Rainer; Kiss, István Z.; Neddermeyer, Jan C. is a scholarly article available to read on EtoBox.

What is On the Relationship Between the Theory of Cointegration and the Theory of Phase Synchronization about?

The theory of cointegration has been a 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 many 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. Apart from phase jumps, a stochastic version of the Kuramoto equations can be approximated by a cointegrated system of difference equations. 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 study two examples on a unidirectionally coupl

Author

Dahlhaus, Rainer; Kiss, István Z.; Neddermeyer, Jan C.

Published

2012

Language

EN