Parameter Estimation for Linear Fractional Stable Noise Process

Over the past few years, scaling phenomena involving self-similarity and heavy-tailed distributions have attracted the interest of various researchers in telecommunications and networks. In this paper, we study the linear fractional stable noise (LFSN) which exhibits both long-range dependence and heavy tails property. LFSN can be represented as a linear process with weight coefficients and α-stable random variables. The coefficients of the linear process are determined by a kernel function and depend on five parameters. This paper focuses on estimating two unknown parameters a and b. Based on minimizing square errors, several methods for estimating these two parameters are presented. Detailed tables and graphs have been included in extensive simulations which show the methods are good estimates.

[1]  Walter Willinger,et al.  Long-range dependence in variable-bit-rate video traffic , 1995, IEEE Trans. Commun..

[2]  Ioannis A. Koutrouvelis,et al.  Regression-Type Estimation of the Parameters of Stable Laws , 1980 .

[3]  Sidney I. Resnick,et al.  Limit Theory for Moving Averages of Random Variables with Regularly Varying Tail Probabilities , 1985 .

[4]  Chrysostomos L. Nikias,et al.  Fast estimation of the parameters of alpha-stable impulsive interference , 1996, IEEE Trans. Signal Process..

[5]  T. Mikosch.  Periodogram estimates from heavy-tailed data , 1998 .

[6]  Svetlozar T. Rachev,et al.  Stable Paretian modeling in finance: some empirical and theoretical aspects , 1998 .

[7]  Richard A. Davis,et al.  Limit Theory for the Sample Covariance and Correlation Functions of Moving Averages , 1986 .

[8]  Richard T. Baillie,et al.  Long memory processes and fractional integration in econometrics , 1996 .

[9]  Stephen Bates,et al.  Traffic characterisation and modelling for call admission control schemes on asynchronous transfer mode networks , 1997 .

[10]  C. Klüppelberg,et al.  PARAMETER-ESTIMATION FOR ARMA MODELS WITH INFINITE VARIANCE INNOVATIONS , 1995 .

[11]  Murad S. Taqqu,et al.  Some long‐run properties of rainfall records in Italy , 1996 .

[12]  Dimitrios Hatzinakos,et al.  Network heavy traffic modeling using α-stable self-similar processes , 2001, IEEE Trans. Commun..

[13]  Walter Willinger,et al.  Self-Similarity in High-Speed Packet Traffic: Analysis and Modeling of Ethernet Traffic Measurements , 1995 .

[14]  C. Mallows,et al.  A Method for Simulating Stable Random Variables , 1976 .

[15]  Patrice Abry,et al.  A Wavelet-Based Joint Estimator of the Parameters of Long-Range Dependence , 1999, IEEE Trans. Inf. Theory.

[16]  M. Taqqu,et al.  Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation, and simulation , 1997 .

[17]  J. McCulloch,et al.  Simple consistent estimators of stable distribution parameters , 1986 .

[18]  Murad S. Taqqu,et al.  Robustness of whittle-type estimators for time series with long-range dependence , 1997 .

[19]  Sidney I. Resnick,et al.  More limit theory for the sample correlation function of moving averages , 1985 .

[20]  D. Applebaum.  Stable non-Gaussian random processes , 1995, The Mathematical Gazette.

[21]  R. Adler,et al.  A practical guide to heavy tails: statistical techniques and applications , 1998 .

[22]  Steve McLaughlin,et al.  The estimation of stable distribution parameters from teletraffic data , 2000, IEEE Trans. Signal Process..

[23]  Mircea Grigoriu,et al.  Applied non-Gaussian processes : examples, theory, simulation, linear random vibration, and MATLAB solutions , 1995 .

[24]  Murad S. Taqqu.  The Modelling of Ethernet Data and of Signals that are Heavy‐tailed with Infinite Variance* , 2002 .