Subordinated Exchange Rate Models: Evidence for Heavy Tailed Distributions and Long-Range Dependence

Mathematical and Computer Modelling, Vol. 34, No. 9-11, pp. 955-1001, 2001

70 Pages Posted: 15 Oct 2004

See all articles by Carlo Marinelli

Carlo Marinelli

University of Bonn - Institut fuer Angewandte Mathematik

Svetlozar Rachev

Texas Tech University

Richard Roll

California Institute of Technology

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 the instrinsic 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 subordinated to an alpha-stable Levy motion (possibly fractional stable) by a long-memory intrinsic time process with Weibull distributed increments.

Suggested Citation

Marinelli, Carlo and Rachev, Svetlozar and Roll, Richard W., Subordinated Exchange Rate Models: Evidence for Heavy Tailed Distributions and Long-Range Dependence. Mathematical and Computer Modelling, Vol. 34, No. 9-11, pp. 955-1001, 2001, Available at SSRN: https://ssrn.com/abstract=603524

Carlo Marinelli (Contact Author)

University of Bonn - Institut fuer Angewandte Mathematik ( email )

Wegelerstr. 6
53115 Bonn
Germany

Svetlozar Rachev

Texas Tech University ( email )

Dept of Mathematics and Statistics
Lubbock, TX 79409
United States
631-662-6516 (Phone)

Richard W. Roll

California Institute of Technology ( email )

1200 East California Blvd
Mail Code: 228-77
Pasadena, CA 91125
United States
626-395-3890 (Phone)
310-836-3532 (Fax)

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