Long‐range dependence

Long‐range dependence (LRD) refers to dependence structures that decay slowly with increasing distance. Mathematically this leads to limit theorems that differ from the short‐memory case, and to major corrections of standard statistical methods. Here, a brief overview of the probabilistic foundations and statistical methods is given. We focus on how LRD is defined, which typical models may generate LRD, how to do statistical inference for stationary and nonstationary long‐memory models, and how to distinguish between LRD and alternative models that may mimic long‐memory behavior.