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Systematic inference of the long-range dependence and heavy-tail distribution parameters of ARFIMA models

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  • Graves, Timothy
  • Franzke, Christian L.E.
  • Watkins, Nicholas W.
  • Gramacy, Robert B.
  • Tindale, Elizabeth

Abstract

Long-Range Dependence (LRD) and heavy-tailed distributions are ubiquitous in natural and socio-economic data. Such data can be self-similar whereby both LRD and heavy-tailed distributions contribute to the self-similarity as measured by the Hurst exponent. Some methods widely used in the physical sciences separately estimate these two parameters, which can lead to estimation bias. Those which do simultaneous estimation are based on frequentist methods such as Whittle’s approximate maximum likelihood estimator. Here we present a new and systematic Bayesian framework for the simultaneous inference of the LRD and heavy-tailed distribution parameters of a parametric ARFIMA model with non-Gaussian innovations. As innovations we use the α-stable and t-distributions which have power law tails. Our algorithm also provides parameter uncertainty estimates. We test our algorithm using synthetic data, and also data from the Geostationary Operational Environmental Satellite system (GOES) solar X-ray time series. These tests show that our algorithm is able to accurately and robustly estimate the LRD and heavy-tailed distribution parameters.

Suggested Citation

  • Graves, Timothy & Franzke, Christian L.E. & Watkins, Nicholas W. & Gramacy, Robert B. & Tindale, Elizabeth, 2017. "Systematic inference of the long-range dependence and heavy-tail distribution parameters of ARFIMA models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 60-71.
  • Handle: RePEc:eee:phsmap:v:473:y:2017:i:c:p:60-71
    DOI: 10.1016/j.physa.2017.01.028
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    References listed on IDEAS

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    1. Stilian Stoev & Murad S. Taqqu, 2005. "Asymptotic self‐similarity and wavelet estimation for long‐range dependent fractional autoregressive integrated moving average time series with stable innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(2), pages 211-249, March.
    2. McCulloch, J Huston, 1997. "Measuring Tail Thickness to Estimate the Stable Index Alpha: A Critique," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 74-81, January.
    3. Nolan, John P., 1998. "Parameterizations and modes of stable distributions," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 187-195, June.
    4. Menn, Christian & Rachev, Svetlozar T., 2006. "Calibrated FFT-based density approximations for [alpha]-stable distributions," Computational Statistics & Data Analysis, Elsevier, vol. 50(8), pages 1891-1904, April.
    5. Shimotsu, Katsumi & Phillips, Peter C.B., 2006. "Local Whittle estimation of fractional integration and some of its variants," Journal of Econometrics, Elsevier, vol. 130(2), pages 209-233, February.
    6. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    7. Burnecki, Krzysztof & Klafter, Joseph & Magdziarz, Marcin & Weron, Aleksander, 2008. "From solar flare time series to fractional dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1077-1087.
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    Cited by:

    1. Steven D. Silver & Marko Raseta, 2021. "An ARFIMA multi-level model of dual-component expectations in repeated cross-sectional survey data," Empirical Economics, Springer, vol. 60(2), pages 683-699, February.
    2. Pietro Murialdo & Linda Ponta & Anna Carbone, 2020. "Long-Range Dependence in Financial Markets: a Moving Average Cluster Entropy Approach," Papers 2004.14736, arXiv.org.
    3. Gajda, Janusz & Bartnicki, Grzegorz & Burnecki, Krzysztof, 2018. "Modeling of water usage by means of ARFIMA–GARCH processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 644-657.

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