  We study the dynamics of the linear and non-linear serial dependencies in
financial time series in a rolling window framework. In particular, we focus on
the detection of episodes of statistically significant two- and three-point
correlations in the returns of several leading currency exchange rates that
could offer some potential for their predictability. We employ a rolling window
approach in order to capture the correlation dynamics for different window
lengths and analyze the distributions of periods with statistically significant
correlations. We find that for sufficiently large window lengths these
distributions fit well to power-law behavior. We also measure the
predictability itself by a hit rate, i.e. the rate of consistency between the
signs of the actual returns and their predictions, obtained from a simple
correlation-based predictor. It is found that during these relatively brief
periods the returns are predictable to a certain degree and the predictability
depends on the selection of the window length.
