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Quantitatively investigating the locally weak stationarity of modified multifractional Gaussian noise

Listed author(s):
  • Li, Ming
  • Zhao, Wei
Registered author(s):

    We suggest that there exists a critical point H=0.70 of the local Hölder exponent H(t) for describing the weak stationary (stationary for short) property of the modified multifractional Gaussian noise (mmGn) from the point of view of engineering. More precisely, when H(t)>0.70 for t∈[0,∞], the stationarity of mmGn is conditional, relying on the variation ranges of H(t). When H(t)≤0.70, on the other side, mmGn is unconditionally stationary, yielding a consequence that short-memory mmGn is stationary. In addition, for H(t)>0.70, we introduce the concept of stationary range denoted by (Hmin,Hmax). It means that Corr[r(τ;H(t1)),r(τ;H(t2))]≥0.70 if H(t1), H(t2)∈(Hmin,Hmax), where r(τ;H(t1)) and r(τ;H(t2)) are the autocorrelation functions of mmGn with H(t1) and H(t2) for t1≠t2, respectively, and Corr[r(τ;H(t1)),r(τ;H(t2))] is the correlation coefficient between r(τ;H(t1)) and r(τ;H(t2)). We present a set of stationary ranges, which may be used for a quantitative description of the local stationarity of mmGn. A case study is demonstrated for applying the present method to testing the stationarity of a real-traffic trace.

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    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 391 (2012)
    Issue (Month): 24 ()
    Pages: 6268-6278

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    Handle: RePEc:eee:phsmap:v:391:y:2012:i:24:p:6268-6278
    DOI: 10.1016/j.physa.2012.07.043
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    1. Masugi, Masao, 2004. "Detrended fluctuation analysis of IP-network traffic using a two-dimensional topology map," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(3), pages 664-678.
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    6. Li, Ming & Lim, S.C., 2008. "Modeling network traffic using generalized Cauchy process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(11), pages 2584-2594.
    7. Stanley, H.E. & Amaral, L.A.N. & Goldberger, A.L. & Havlin, S. & Ivanov, P.Ch. & Peng, C.-K., 1999. "Statistical physics and physiology: Monofractal and multifractal approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 270(1), pages 309-324.
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