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Synchronization is a phenomenon in which a pair of fluctuations adjust theirrhythms when interacting with each other. We measure the degree ofsynchronization between the U.S. dollar (USD) and euro exchange rates andbetween the USD and Japanese yen exchange rates on the basis of purchasingpower parity (PPP) over time. We employ a method of synchronization analysisusing 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, suggestingthe establishment of PPP. The degree of synchronization does not remain highacross periods with economic events with asymmetric effects, such as the U.S.real estate bubble.

Synchronization analysis between exchange rates on the basis of purchasing power parity using the Hilbert transform