Scandinavian Working Papers in Business Administration
Working Papers,
Örebro University, School of Business
No 2019:9: Linear Fractional Stable Motion with the RLFSM R Package
Stepan Mazur () and Dmitry Otryakhin ()
Additional contact information
Stepan Mazur: Örebro University School of Business, Postal: Örebro University, School of Business, SE - 701 82 ÖREBRO, Sweden
Dmitry Otryakhin: Aarhus University, Postal: Department of Mathematics, Ny Munkegade 118, building 1535, 315, 8000 Aarhus C, Denmark
Abstract: Linear fractional stable motion is a type of a stochastic integral driven by symmetric alpha-stable L´evy motion. The integral could be considered as a non-Gaussian analogue of the fractional Brownian motion. The present paper discusses R package rlfsm created for numerical procedures with the linear fractional stable motion. It is a set of tools for simulation of these processes as well as performing statistical inference and simulation studies on them. We introduce: tools that we developed to work with that type of motions as well as methods and ideas underlying them. Also we perform numerical experiments to show finite-sample behavior of certain estimators of the integral, and give an idea of how to envelope workflow related to the linear fractional stable motion in S4 classes and methods. Supplementary materials, including codes for numerical experiments, are available online. rlfsm could be found on CRAN and gitlab.
Keywords: Fractional processes; limit theorems; parametric estimation; stochastic simulation; stable motion
32 pages, November 13, 2019
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