A New Stochastic Process with Long-Range Dependence

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.

Keywords

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