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Asymptotic self‐similarity and wavelet estimation for long‐range dependent fractional autoregressive integrated moving average time series with stable innovations

Author

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  • Stilian Stoev
  • Murad S. Taqqu

Abstract

. Methods for parameter estimation in the presence of long‐range dependence and heavy tails are scarce. Fractional autoregressive integrated moving average (FARIMA) time series for positive values of the fractional differencing exponent d can be used to model long‐range dependence in the case of heavy‐tailed distributions. In this paper, we focus on the estimation of the Hurst parameter H = d + 1/α for long‐range dependent FARIMA time series with symmetric α‐stable (1

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:26:y:2005:i:2:p:211-249
    DOI: 10.1111/j.1467-9892.2005.00399.x
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    References listed on IDEAS

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    Cited by:

    1. Beran, Jan, 2007. "On parameter estimation for locally stationary long-memory processes," CoFE Discussion Papers 07/13, University of Konstanz, Center of Finance and Econometrics (CoFE).
    2. Harry Pavlopoulos & George Chronis, 2023. "On highly skewed fractional log‐stable noise sequences and their application," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(4), pages 337-358, July.
    3. Jaesik Jeong & Marina Vannucci & Kyungduk Ko, 2013. "A Wavelet-Based Bayesian Approach to Regression Models with Long Memory Errors and Its Application to fMRI Data," Biometrics, The International Biometric Society, vol. 69(1), pages 184-196, March.
    4. 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.
    5. Ayache, Antoine & Hamonier, Julien, 2012. "Linear fractional stable motion: A wavelet estimator of the α parameter," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1569-1575.
    6. P. S. Sephton, 2010. "Unit roots and purchasing power parity: another kick at the can," Applied Economics, Taylor & Francis Journals, vol. 42(27), pages 3439-3453.

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