A New Stochastic Process with Long-Range Dependence

Authors

Sung Ik Kim^{1, *,} , Young Shin Kim²

¹College of Business, Louisiana State University Shreveport, 1 University Place, Shreveport, LA 71115, USA

²College of Business, Stony Brook University, 100 Nicolls Road., Stony Brook, NY 11794, USA

^*Corresponding author. Email: sung.kim@lsus.edu

DOI

10.2991/jsta.d.200923.001How to use a DOI?

Keywords

Generalized hyperbolic process; Lévy process; Time-changed Brownian motion; Long-range dependence; Fractional Brownian motion

Abstract

In this paper, we introduce a fractional Generalized Hyperbolic process, a new stochastic process with long-range dependence obtained by subordinating fractional Brownian motion to a fractional Generalized Inverse Gaussian process. The basic properties and covariance structure between the elements of the processes are discussed, and we present numerical methods to generate the sample paths for the processes.

Copyright

© 2020 The Authors. Published by Atlantis Press B.V.

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Sung Ik Kim
AU  - Young Shin Kim
PY  - 2020
DA  - 2020/10/06
TI  - A New Stochastic Process with Long-Range Dependence
JO  - Journal of Statistical Theory and Applications
SP  - 432
EP  - 438
VL  - 19
IS  - 3
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.d.200923.001
DO  - 10.2991/jsta.d.200923.001
ID  - Kim2020
ER  -