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

Authors:
C. Marinelli;S. T. Rachev;R. Roll
Affiliations:
Department of Electronics and Computer Science University of Padova, via Gradenigo 6A 35131 Padova, Italy;Institute of Statistics and Mathematical Economics University of Karlsruhe, Kollegium am Schloss, Bau II D-76128 Karlsruhe, Germany;Anderson Schol of Management, University of California Los Angeles, CA, U.S.A.
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2001

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Abstract

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 Levy 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 @a-stable Levy motion S(t) (possibly fractional stable) by a long-memory intrinsic time process T(t) with Weibull-distributed increments.