On the nonstationarity of the exchange rate process
We empirically investigate the nonstationarity property of the USD–JPY exchange rate by using a high frequency data set spanning 8years. We perform a statistical test of strict stationarity based on the two-sample Kolmogorov–Smirnov test for the absolute price changes, and Pearson's chi square test for the number of successive price changes in the same direction, and find statistically significant evidence of nonstationarity. Further, we study the recurrence intervals between the days in which nonstationarity occurs and find that the distribution of recurrence intervals is well approximated by an exponential distribution. In addition, we find that the mean conditional recurrence interval hTjT0i is independent of the previous recurrence interval T0. These findings indicate that the recurrence intervals are characterized by a Poisson process. We interpret this observation as a reflection of the Poisson property regarding the arrival of news.
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