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A Note on Bayesian Inference for Long-Range Dependence of a Stationary Two-State Process

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Interdisciplinary Bayesian Statistics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 118))

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Abstract

In this work we propose a Bayesian approach for selecting the range of a stationary process with two states. The analysis is based on approximate posterior distributions of the Hurst index obtained from a likelihood-free method. Our empirical study shows that a main advantage of our approach, along with its of simplicity, is the possibility of obtaining an approximate sample of the posterior distribution on the Hurst index, thus providing better estimates. Furthermore, there is no need for Gaussian nor asymptotic assumptions.

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Acknowledgements

The first author is a PhD student with CNPq grant at the University of São Paulo. For the second author, this work was produced as part of the activities of FAPESP Center for Neuromathematics (grant 2013/ 07699-0, S. Paulo Research Foundation).

Author information

Authors and Affiliations

  1. Institute of Mathematics and Statistics, University of São Paulo, São Paulo, Brazil

    Plinio L. D. Andrade

  2. Institute of Mathematics and Statistics, University of Campinas, Campinas, Brazil

    Laura L. R. Rifo

Authors
  1. Plinio L. D. Andrade
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  2. Laura L. R. Rifo
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Corresponding author

Correspondence to Plinio L. D. Andrade .

Editor information

Editors and Affiliations

  1. Federal University of Sao Carlos, Sao Carlos, Brazil

    Adriano Polpo

  2. University of Sao Paulo, Sao Carlos, Brazil

    Francisco Louzada

  3. Campinas State University, Campinas, Brazil

    Laura L. R. Rifo

  4. Dept. of Applied Mathematics, University of Sao Paulo Institute of Mathematics and Statistics, Sao Paulo, São Paulo, Brazil

    Julio M. Stern

  5. School of Arts, Sciences and Humanities, University of Sao Paulo, Sao Paulo, São Paulo, Brazil

    Marcelo Lauretto

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Andrade, P., Rifo, L. (2015). A Note on Bayesian Inference for Long-Range Dependence of a Stationary Two-State Process. In: Polpo, A., Louzada, F., Rifo, L., Stern, J., Lauretto, M. (eds) Interdisciplinary Bayesian Statistics. Springer Proceedings in Mathematics & Statistics, vol 118. Springer, Cham. https://doi.org/10.1007/978-3-319-12454-4_25

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