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

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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

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  • 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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    1. Kokoszka, Piotr S. & Taqqu, Murad S., 1995. "Fractional ARIMA with stable innovations," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 19-47, November.
    2. Clifford M. Hurvich & Rohit Deo & Julia Brodsky, 1998. "The mean squared error of Geweke and Porter‐Hudak's estimator of the memory parameter of a long‐memory time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(1), pages 19-46, January.
    3. Kokoszka, Piotr S. & Taqqu, Murad S., 1996. "Infinite variance stable moving averages with long memory," Journal of Econometrics, Elsevier, vol. 73(1), pages 79-99, July.
    4. Cambanis, Stamatis & Hardin, Clyde D. & Weron, Aleksander, 1987. "Ergodic properties of stationary stable processes," Stochastic Processes and their Applications, Elsevier, vol. 24(1), pages 1-18, February.
    5. Delbeke, Lieve & Abry, Patrice, 2000. "Stochastic integral representation and properties of the wavelet coefficients of linear fractional stable motion," Stochastic Processes and their Applications, Elsevier, vol. 86(2), pages 177-182, April.
    6. Jean‐Marc Bardet, 2000. "Testing for the Presence of Self‐Similarity of Gaussian Time Series Having Stationary Increments," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(5), pages 497-515, September.
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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. 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.
    3. 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.
    4. 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.
    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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