The fractional multivariate normal tempered stable process

In this paper, the multivariate process having long-range dependency is presented. The process is defined by the time-changed fractional Brownian motion whose subordinator is given by the fractional tempered stable subordinator. The fractional tempered stable subordinator is a generalization of the non-decreasing tempered stable process with long-range dependence. The multivariate process allows for (1) the long-range dependence in the endogenous noise, (2) the long-range dependence in time or the volatility, (3) the fat-tailed marginal distribution, and (4) an asymmetric dependence structure between elements. Numerical methods to generating sample paths for the process are discussed.