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Long-range correlation: Difference between revisions
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=== Experimental determination === | === Experimental determination === | ||
It can be shown that determining the long-range behaviour of the correlation function directly from γ<sub>XY</sub> is not a good idea, due to its sensitivity to noise.<ref>[[doi:10.1063/1.873192|B.A. Carreras, D.E. Newman, B.Ph. van Milligen, and C. Hidalgo, ''Long-range time dependence in the cross-correlation function'', Phys. Plasmas '''6''' (1999) 485]]</ref> | It can be shown that determining the long-range behaviour of the correlation function directly from γ<sub>XY</sub> is not a good idea, due to its sensitivity to noise.<ref>[[doi:10.1063/1.873192|B.A. Carreras, D.E. Newman, B.Ph. van Milligen, and C. Hidalgo, ''Long-range time dependence in the cross-correlation function'', Phys. Plasmas '''6''' (1999) 485]]</ref> | ||
Rather, techniques to determine the [[:Wikipedia:Hurst exponent|Hurst exponent]], such as the [[:Wikipedia:Rescaled range|Rescaled Range]]<ref>[[doi:10.1103/PhysRevLett.80.4438|B.A. Carreras, B. van Milligen, M.A. Pedrosa, et al., ''Long-Range Time Correlations in Plasma Edge Turbulence'', Phys. Rev. Lett. '''80''' (1998) 4438]]</ref> or Structure Functions<ref>[[doi:10.1063/1.1459707|M. Gilmore, C.X. Yu, T.L. Rhodes, and W.A. Peebles, ''Investigation of rescaled range analysis, the Hurst exponent, and long-time correlations in plasma turbulence'', Phys. Plasmas '''9''' (2002) 1312]]</ref> should be used to determine long-range correlations in data series. | Rather, techniques to determine the [[:Wikipedia:Hurst exponent|Hurst exponent]], such as the [[:Wikipedia:Rescaled range|Rescaled Range]]<ref>[[doi:10.1103/PhysRevLett.80.4438|B.A. Carreras, B. van Milligen, M.A. Pedrosa, et al., ''Long-Range Time Correlations in Plasma Edge Turbulence'', Phys. Rev. Lett. '''80''' (1998) 4438]]</ref><ref>[[doi:10.1063/1.873490|B.A. Carreras, B.Ph. van Milligen, M.A. Pedrosa, et al., ''Experimental evidence of long-range correlations and self-similarity in plasma fluctuations'', Phys. Plasmas 6 (1999) 1885]]</ref> or Structure Functions<ref>[[doi:10.1063/1.1459707|M. Gilmore, C.X. Yu, T.L. Rhodes, and W.A. Peebles, ''Investigation of rescaled range analysis, the Hurst exponent, and long-time correlations in plasma turbulence'', Phys. Plasmas '''9''' (2002) 1312]]</ref> should be used to determine long-range correlations in data series. | ||
== See also == | == See also == | ||