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 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.