  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 coupled R\"ossler-Lorenz
system and on electrochemical oscillators. The methods from cointegration may
also be used to investigate phase synchronization in complex networks.
Conversely, there are many interesting results on phase synchronization which
may inspire new research on cointegration.
