On the Nonstationarity of the Exchange Rate Process
We empirically investigate the nonstationarity property of the dollar-yen exchange rate by using an eight year span of high frequency data set. We perform a statistical test of strict stationarity based on the two-sample KolmogorovSmirnov test for the absolute price changes, and the Pearson’s chi-square test for the number of successive price changes in the same direction, and find statistically significant evidence of nonstationarity. We further 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. Also, we find that the mean conditional recurrence interval 〈T|T0〉 is independent of the previous recurrence interval T0. These findings indicate that the recurrence intervals is characterized by a Poisson process. We interpret this as reflecting the Poisson property regarding the arrival of news.
Financial time series data have been extensively investigated using a wide
variety of methods in econophysics. These studies tend to assume, explicitly
or implicitly, that a time series is stationary, since stationarity is a requirement
for most of the mathematical theories underlying time series analysis.
However, despite its nearly universal assumption, there is little previous studies
that seek to test stationarity in a reliable manner. (Toth1a et al. (2010)).