Intraday volatility and scaling in high frequency foreign exchange markets

Recent reports suggest that the stochastic process underlying financial time series is nonstationary with nonstationary increments. Therefore, time averaging techniques through sliding intervals are inappropriate and ensemble methods have been proposed. Using daily ensemble averages we analyze two different measures of intraday volatility, trading frequency and the mean square fluctuation of increments for the three most active FX markets; we find that both measures indicate that the underlying stochastic dynamics exhibits nonstationary increments. We show that the two volatility measures are equivalent. In each market we find three time intervals during the day where the mean square fluctuation of increments can be fit by power law scaling in time. The scaling indices in the intervals are different, but independent of the FX market under study. We also find that the fluctuations in return in these intervals lie on exponential distributions.