Local Analysis of Self-Similarity - The LASS tool is designed to handle time series that have long-range dependence and are long enough that some parts are essentially stationary, while others exhibit non-stationarity, which is either deterministic or stochastic in nature. The tool exploits wavelets to analyze the local dependence structure in the data over a set of windows. It can be used to visualize local deviations from self-similar, long-range dependence scaling and to provide reliable local estimates of the Hurst exponents. The tool, which is illustrated by using a trace of Internet traffic measurements, can also be applied to economic time series. In addition, a median-based wavelet spectrum is introduced. It yields robust local or global estimates of the Hurst parameter that are less susceptible to local non-stationarity. The software tools are freely available and their use is described in an appendix.

References in zbMATH (referenced in 30 articles , 1 standard article )

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  1. Basse-O’connor, Andreas; Grønbæk, Thorbjørn; Podolskij, Mark: Local asymptotic self-similarity for heavy tailed harmonizable fractional Lévy motions (2021)
  2. Knight, Marina I.; Nason, Guy P.; Nunes, Matthew A.: A wavelet lifting approach to long-memory estimation (2017)
  3. Rezakhah, Saeid; Maleki, Yasaman: Discretization of continuous time discrete scale invariant processes: estimation and spectra (2016)
  4. Kouamo, O.; Lévy-Leduc, C.; Moulines, E.: Central limit theorem for the robust log-regression wavelet estimation of the memory parameter in the Gaussian semi-parametric context (2013)
  5. Song, Li; Bondon, Pascal: Structural changes estimation for strongly dependent processes (2013)
  6. Clausel, Marianne; Nicolay, Samuel: A wavelet characterization for the upper global Hölder index (2012)
  7. Das, Saptarshi; Pan, Indranil: Fractional order signal processing. Introductory concepts and applications. (2012)
  8. Mondal, Debashis; Percival, Donald B.: (M)-estimation of wavelet variance (2012)
  9. Chen, Yangquan; Sun, Rongtao; Zhou, Anhong: An improved Hurst parameter estimator based on fractional Fourier transform (2010) ioport
  10. Bekmaganbetov, K.; Nursultanov, E.: Interpolation of Besov (B^\sigmaq_p\tau) and Lizorkin-Triebel (F^\sigmaq_p\tau) spaces (2009)
  11. Faÿ, Gilles; Moulines, Eric; Roueff, François; Taqqu, Murad S.: Estimators of long-memory: Fourier versus wavelets (2009)
  12. Kranz, Horst; Oberschelp, Walter: Mechanical memorizing and coding around 1430. Johannes Fontanas Tractatus de instrumentis artis memorie (2009)
  13. Roueff, F.; Taqqu, M. S.: Asymptotic normality of wavelet estimators of the memory parameter for linear processes (2009)
  14. Barbosa, Susana M.; Silva, Maria Eduarda; Fernandes, Maria Joana: Time series analysis of sea-level records: characterising long-term variability (2008)
  15. Coeurjolly, Jean-François: Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles (2008)
  16. Mielniczuk, J.; Wojdyłło, P.: Estimation of Hurst exponent revisited (2007)
  17. Park, Cheolwoo; Godtliebsen, Fred; Taqqu, Murad; Stoev, Stilian; Marron, J. S.: Visualization and inference based on wavelet coefficients, SiZer and SiNos (2007)
  18. Pollock, D. S. G. (ed.); Proietti, Tommaso (ed.): Editorial: 2nd special issue on statistical signal extraction and filtering (2007)
  19. Shen, Haipeng; Zhu, Zhengyuan; Lee, Thomas C. M.: Robust estimation of the self-similarity parameter in network traffic using wavelet transform (2007)
  20. Biermé, Hermine; Estrade, Anne: Poisson random balls: self-similarity and X-ray images (2006)

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