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Subordinated exchange rate models: Evidence for heavy tailed distributions and long-range dependence. (English) Zbl 1006.60011

Authors’ 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 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 \(\alpha\)-stable Lévy motion \(S(t)\) (possibly fractional stable) by a long-memory intrinsic time process \(T(t)\) with Weibull-distributed increments.

MSC:

60E05 Probability distributions: general theory
91B24 Microeconomic theory (price theory and economic markets)

Software:

STABLE; longmemo
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