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Ambiguities in estimates of critical exponents for long-range dependent processes

Author

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  • Duffy, Ken
  • King, Christopher
  • Malone, David

Abstract

In this article, we show that the Hurst parameter and a well-known wavelet estimator fail to distinguish on/off models with substantially different distributions of on-times. We identify the problem as arising when standard power spectrum techniques, which are well-defined for commonly considered processes, are applied to processes with extremely heavy tailed on-times. We provide an elementary mechanism whereby such extremely heavy-tailed on-time processes arise in a simple queuing model.

Suggested Citation

  • Duffy, Ken & King, Christopher & Malone, David, 2007. "Ambiguities in estimates of critical exponents for long-range dependent processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 43-52.
    • Handle: RePEc:eee:phsmap:v:377:y:2007:i:1:p:43-52
    DOI: 10.1016/j.physa.2006.11.015
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    References listed on IDEAS

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    1. Takayasu, Misako & Takayasu, Hideki & Fukuda, Kensuke, 2000. "Dynamic phase transition observed in the Internet traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 277(1), pages 248-255.
    2. Fukuda, Kensuke & Takayasu, Hideki & Takayasu, Misako, 2000. "Origin of critical behavior in Ethernet traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(1), pages 289-301.
    3. Hurvich, Clifford M. & Soulier, Philippe, 2002. "Testing For Long Memory In Volatility," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1291-1308, December.
    4. David Heath & Sidney Resnick & Gennady Samorodnitsky, 1998. "Heavy Tails and Long Range Dependence in On/Off Processes and Associated Fluid Models," Mathematics of Operations Research, INFORMS, vol. 23(1), pages 145-165, February.
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