Subordinated exchange rate models: evidence for heavy tailed distributions and long-range dependence

We investigate the main properties of high-frequency exchange rate data in the setting of stochastic subordination and stable modeling, focusing on heavy-tailedness and long memory, together with their dependence on the sampling period. We show that the intrinsic time process exhibits strong long-range dependence and has increments well described by a Weibull law, while the return series in intrinsic time has weak long memory and is well approximated by a stable Lévy motion. We also show that the stable domain of attraction offers a good fit to the returns in physical time, which leads us to consider as a realistic model for exchange rate data a process Z(t) subordinated to an α-stable Lévy motion S(t) (possibly fractional stable) by a long-memory intrinsic time process T(t) with Weibull-distributed increments.