Long-range dependence and approximate Bayesian computation |
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Authors: | P. Andrade L. Rifo |
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Affiliation: | 1. Institute of Mathematics and Statistics, University of S?o Paulo, S?o Paulo, Brazilplinio@ime.usp.br;3. Institute of Mathematics and Statistics, University of Campinas, Campinas, Brazil |
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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. |
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Keywords: | Bayesian inference Entropy Hurst index Likelihood-free method Long-range dependence |
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