
On the Nonstationarity of the Exchange Rate Process
Abstract
We empirically investigate the nonstationarity property of the dollaryen exchange rate by using an eight year span of high frequency data set. We perform a statistical test of strict stationarity based on the twosample KolmogorovSmirnov test for the absolute price changes, and the Pearson’s chisquare 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 wellapproximated by an exponential distribution. Also, we find that the mean conditional recurrence interval 〈TT_{0}〉 is independent of the previous recurrence interval T_{0}. 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.
Introduction
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)).