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 26 articles , 1 standard article )

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  1. Rezakhah, Saeid; Maleki, Yasaman: Discretization of continuous time discrete scale invariant processes: estimation and spectra (2016)
  2. 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)
  3. Clausel, Marianne; Nicolay, Samuel: A wavelet characterization for the upper global Hölder index (2012)
  4. Das, Saptarshi; Pan, Indranil: Fractional order signal processing. Introductory concepts and applications. (2012)
  5. Mondal, Debashis; Percival, Donald B.: $M$-estimation of wavelet variance (2012)
  6. Chen, Yangquan; Sun, Rongtao; Zhou, Anhong: An improved Hurst parameter estimator based on fractional Fourier transform (2010)
  7. Bekmaganbetov, K.; Nursultanov, E.: Interpolation of Besov $B^\sigma q_p\tau$ and Lizorkin-Triebel $F^\sigma q_p\tau$ spaces (2009)
  8. Kranz, Horst; Oberschelp, Walter: Mechanical memorizing and coding around 1430. Johannes Fontanas Tractatus de instrumentis artis memorie (2009)
  9. Roueff, F.; Taqqu, M.S.: Asymptotic normality of wavelet estimators of the memory parameter for linear processes (2009)
  10. Barbosa, Susana M.; Silva, Maria Eduarda; Fernandes, Maria Joana: Time series analysis of sea-level records: characterising long-term variability (2008)
  11. Coeurjolly, Jean-François: Hurst exponent estimation of locally self-similar Gaussian processes using sample quantiles (2008)
  12. Mielniczuk, J.; Wojdyłło, P.: Estimation of Hurst exponent revisited (2007)
  13. Park, Cheolwoo; Godtliebsen, Fred; Taqqu, Murad; Stoev, Stilian; Marron, J.S.: Visualization and inference based on wavelet coefficients, sizer and sinos (2007)
  14. Pollock, D.S.G.; Proietti, Tommaso: 2nd special issue on statistical signal extraction and filtering (2007)
  15. Shen, Haipeng; Zhu, Zhengyuan; Lee, Thomas C.M.: Robust estimation of the self-similarity parameter in network traffic using wavelet transform (2007)
  16. Biermé, Hermine; Estrade, Anne: Poisson random balls: self-similarity and X-ray images (2006)
  17. Liu, Chunfeng; Yang, Di; Wang, Juan: $k$-gracefulness and sequential features of two lass graphs (2006)
  18. Stoev, Stilian; Taqqu, Murad S.; Park, Cheolwoo; Michailidis, George; Marron, J.S.: LASS: a tool for the local analysis of self-similarity (2006)
  19. Adámek, Jiří; Milius, Stefan; Velebil, Jiří: A general final coalgebra theorem (2005)
  20. Lass, B.: The $N$-dimensional matching polynomial (2005)

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