درباره سیالیت روند نرخ ارز

We empirically investigate the nonstationarity property of the USD–JPY exchange rate by using a high frequency data set spanning 8 years. 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.

In econophysics, financial time series data have been extensively investigated using a wide variety of methods. 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, few previous studies seek to test stationarity in a reliable manner (Tóthla, et al., 2010). For low-frequency financial data (i.e., monthly or daily data), a number of procedures to test stationarity have been advocated and applied to various time series processes in econometrics. Most of them focus on the first two moments of a process; in other words, they test covariance stationarity. These tests work well for normally distributed random variables. However, for high-frequency financial data such as tick-by-tick data, it is well known that price change distributions are fat-tailed and substantially deviate from a normal distribution. These fat-tailed distributions cannot be dealt with by the above stationarity tests. In this paper, we advocate a test for strict stationarity that considers the entire distribution of a process rather than the first two moments of the process, and apply this test to the USD–JPY exchange rate. We describe the data used in this paper in Section 2. In Section 3, we explain our procedure to test stationarity, which is based on the two-sample Kolmogorov–Smirnov test and Pearson's chi-square test. In Section 4, we present the empirical results. In Section 5, we discuss some implications of our results.

First, we compare the distribution of observations in the subsets (h, t) and (h, t′) for every pair of t and t′. This exercise is repeated N0 ∼ 106 times. Then, we count the number of times, which is denoted by N, in which we reject the null hypothesis that the two distributions are identical. Fig. 4 shows the results of this exercise. The y-axis represents N/N0. Note that if the entire time series is stationary, the rejection rate would be 5%. The x-axis represents the hour of the day. The closed symbols represent the result of this exercise for G; the open symbols, for D. We see that for each h, the rejection rate is much higher than the critical value, that is, 5%, indicating that the null hypothesis of stationarity is clearly rejected. We suspect that this is the result of long time correlations in the time series of the absolute value of price changes (volatility clustering). Turning to the results for D, we again find that for each h, the rejection rate is significantly above the critical value. Therefore, we conclude from these exercises that the exchange rate process is not a stationary process.