Long-range dependence and approximate Bayesian computation

ABSTRACT

In this work, we propose a method for estimating the Hurst index, or memory parameter, of a stationary process with long memory in a Bayesian fashion. Such approach provides an approximation for the posterior distribution for the memory parameter and it is based on a simple application of the so-called approximate Bayesian computation (ABC), also known as likelihood-free method. Some popular existing estimators are reviewed and compared to this method for the fractional Brownian motion, for a long-range binary process and for the Rosenblatt process. The performance of our proposal is remarkably efficient.

KEYWORDS:

• Bayesian inference
• Entropy
• Hurst index
• Likelihood-free method
• Long-range dependence

Mathematics Subject Classification:

• Primary 60G18
• Secondary 62M09

Acknowledgments

This article was produced as part of the activities of FAPESP Research, Innovation and Dissemination Center for Neuromathematics (grant 2013/07699-0, São Paulo Research Foundation). The first author is PhD student with CNPq grant no. 141048/2013-1 at the University of São Paulo.