  Synchronization is a phenomenon in which a pair of fluctuations adjust their
rhythms when interacting with each other. We measure the degree of
synchronization between the U.S. dollar (USD) and euro exchange rates and
between the USD and Japanese yen exchange rates on the basis of purchasing
power parity (PPP) over time. We employ a method of synchronization analysis
using the Hilbert transform, which is common in the field of nonlinear science.
We find that the degree of synchronization is high most of the time, suggesting
the establishment of PPP. The degree of synchronization does not remain high
across periods with economic events with asymmetric effects, such as the U.S.
real estate bubble.
