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Robust Wavelet-Domain Estimation of the Fractional Difference Parameter in Heavy-Tailed Time Series: An Empirical Study

Author

Listed:
  • Agnieszka Jach

    (Universidad Carlos III de Madrid)

  • Piotr Kokoszka

    (Utah State University)

Abstract

We investigate the performance of several wavelet-based estimators of the fractional difference parameter. We consider situations where, in addition to long-range dependence, the time series exhibit heavy tails and are perturbed by polynomial and change-point trends. We make detailed study of a wavelet-domain pseudo Maximum Likelihood Estimator (MLE), for which we provide an asymptotic and finite-sample justification. Using numerical experiments, we show that unlike the traditional time-domain estimators, estimators based on the wavelet transform are robust to additive trends and change points in mean, and produce accurate estimates even under significant departures from normality. The Wavelet-domain MLE appears to dominate a regression-based wavelet estimator in terms of smaller root mean squared error. These findings are derived from a simulation study and application to computer traffic traces.

Suggested Citation

  • Agnieszka Jach & Piotr Kokoszka, 2010. "Robust Wavelet-Domain Estimation of the Fractional Difference Parameter in Heavy-Tailed Time Series: An Empirical Study," Methodology and Computing in Applied Probability, Springer, vol. 12(1), pages 177-197, March.
    • Handle: RePEc:spr:metcap:v:12:y:2010:i:1:d:10.1007_s11009-008-9105-3
    DOI: 10.1007/s11009-008-9105-3
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    References listed on IDEAS

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    1. Giraitis, Liudas & Robinson, Peter & Surgailis, Donatas, 2000. "A model for long memory conditional heteroscedasticity," LSE Research Online Documents on Economics 2103, London School of Economics and Political Science, LSE Library.
    2. Giraitis, Liudas & Robinson, Peter M. & Surgailis, Donatas, 2000. "A model for long memory conditional heteroscedasticity," LSE Research Online Documents on Economics 299, London School of Economics and Political Science, LSE Library.
    3. John Geweke & Susan Porter‐Hudak, 1983. "The Estimation And Application Of Long Memory Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(4), pages 221-238, July.
    4. Lobato, Ignacio N & Velasco, Carlos, 2000. "Long Memory in Stock-Market Trading Volume," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 410-427, October.
    5. Robinson, Peter M. & Velasco, Carlos, 2000. "Whittle pseudo-maximum likelihood estimation for nonstationary time series," LSE Research Online Documents on Economics 2273, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. Hongchang Hu & Weifu Hu & Xinxin Yu, 2021. "Pseudo-maximum likelihood estimators in linear regression models with fractional time series," Statistical Papers, Springer, vol. 62(2), pages 639-659, April.
    2. Heni Boubaker, 2020. "Wavelet Estimation Performance of Fractional Integrated Processes with Heavy-Tails," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 473-498, February.

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