Autocorrelation as a source of truncated Levy flights in foreign exchange rates

We suggest that the ultraslow speed of convergence associated with truncated Levy flights (Phys. Rev. Lett. 73 (1994) 2946) may well be explained by autocorrelations in data. We show how a particular type of autocorrelation generates power laws consistent with a truncated Levy flight. Stock exchanges have been suggested to be modeled by a truncated Levy flight (Nature 376 (1995) 46; Physica A 297 (2001) 509; Econom. Bull. 7 (2002) 1). Here foreign exchange rate data are taken instead. Scaling power laws in the "probability of return to the origin" are shown to emerge for most currencies. A novel approach to measure how distant a process is from a Gaussian regime is presented. (C) 2003 Elsevier Science B.V. All rights reserved.