Levy Flights, Autocorrelation, and Slow Convergence
Previously we have put forward that the sluggish convergence of truncated Lévy flights to a Gaussian (Phys. Rev. Lett. 73 (1994) 2946) together with the scaling power laws in their probability of return to the origin (Nature 376 (1995) 46) can be explained by autocorrelation in data (Physica A 323 (2003) 601; Phys. Lett. A 315 (2003) 51). A purpose of this paper is to improve and enlarge the scope of such a result. The role of the autocorrelations in the convergence process as well as the problem of establishing the distance of a given distribution to the Gaussian are analyzed in greater detail. We show that whereas power laws in the second moment can still be explained by linear correlation of pairs, sluggish convergence can now emerge from nonlinear autocorrelations. Our approach is exemplified with data from the British pound–US dollar exchange rate.
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- Figueiredo, Annibal & Gleria, Iram & Matsushita, Raul & Da Silva, Sergio, 2003.
"Autocorrelation as a source of truncated Lévy flights in foreign exchange rates,"
Physica A: Statistical Mechanics and its Applications,
Elsevier, vol. 323(C), pages 601-625.
- Sergio Da Silva, 2004. "Autocorrelation as a Source of Truncated Levy Flights in Foreign Exchange Rates," Finance 0405018, EconWPA.
- Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
- Rafal Weron, 2003.
"Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime,"
- Rafal Weron, 2001. "Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime," HSC Research Reports HSC/01/01, Hugo Steinhaus Center, Wroclaw University of Technology.
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