Quantitatively investigating the locally weak stationarity of modified multifractional Gaussian noise
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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Volume (Year): 391 (2012)
Issue (Month): 24 ()
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- 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.
- Muniandy, S.V. & Lim, S.C. & Murugan, R., 2001. "Inhomogeneous scaling behaviors in Malaysian foreign currency exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 407-428.
- Stanley, H.E. & Buldyrev, S.V. & Goldberger, A.L. & Havlin, S. & Peng, C.-K. & Simons, M., 1993. "Long-range power-law correlations in condensed matter physics and biophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 200(1), pages 4-24.
- Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
- Shang, Pengjian & Lu, Yongbo & Kama, Santi, 2006. "The application of Hölder exponent to traffic congestion warning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 769-776.
- Carbone, A. & Castelli, G. & Stanley, H.E., 2004. "Time-dependent Hurst exponent in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 267-271.
- 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.
- 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.
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