The scientific legacy of Harold Edwin Hurst (1880–1978)

Figures & data

Figure 1. The proliferation of Hurst’s work in different scientific fields.

Table 1. Definitions of Population Range and Adjusted Range.

Denote a series of n random variables as , , …, with sample mean and with E.

Population Range of cumulative departures:

= max – min

Adjusted Range of cumulative departures:

= max – min

Figure 2. Globally averaged annual precipitation calculated from 5° × 5° GHCN (version 2) monthly precipitation dataset for the period 1900–2014 (http://www.ncdc.noaa.gov/temp-and-precip/ghcn-gridded-products/).

Figure 3. Number of citations per year of Hurst’s original paper (bars; adding up to 3752 citations) and papers in which one or more of the phrases “Hurst coefficient”, “Hurst exponent”, “Hurst parameter”, “Hurst effect” or “Hurst Phenomenon” appear (solid line; summing to 22 755 citations). Data from Google Scholar as of March 2014. Notice the logarithmic scale of the vertical axis.

Table 2. Top-cited papers (from journals) with reference to Hurst’s work in different scientific fields (two from each one) and their impact in terms of citations (data from Google Scholar as of March 2014).

Field	Reference	Subject	Citations
Statistics and stochastics
	Mandelbrot and Van Ness (1968) Hosking (1981)	Fractional Brownian motion	5005
		FARIMA model	541
Geophysical sciences
	Mandelbrot and Wallis (1969e) Sadler (1981)^‡	Geophysical records	863
		Sediment accumulation rate	572
Physics
	Voss and Clarke (1975)	Acoustics	414
	Borland (1998)^‡	Diffusion	309
Economics and finance
	Greene and Fielitz (1977) Baillie (1996)	Stock market prices	346
		Econometrics	1282
Medical sciences
	Ellaway (1978)	Neurophysiology	377
	Kobayashi and Musha (1982)	Heartbeat period	656
Biology
	Peng et al. (1992)^‡	Nucleotide sequences	1159
	Arneodo et al. (1996)^‡	DNA sequences	174
Information sciences
	Leland et al. (1993, 1994)	Ethernet traffic	7316*
	Frost and Melamed (1994)	Traffic in telecommunication networks	667
Climate science
	Koutsoyiannis (2003)	Climatic variability	191
	Cohn and Lins (2005)	Trends in climate	202

*This is the sum of the citations of Leland et al. (1993, 1994), referring to two versions of the same paper.

^‡There is no citation to Hurst (1951), but there is a reference to Hurst Coefficient/Phenomenon in the paper.

Mandelbrot, B.B. and Van Ness, J.W., 1968. Fractional Brownian motions, fractional noises and applications. SIAM Reviews, 10 (4), 422–437. doi:10.1137/1010093

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Sadler, P.M., 1981. Sediment accumulation rates and the completeness of stratigraphic sections. Journal of Geology, 89 (5), 569–584. doi:10.1086/628623

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Voss, R.F. and Clarke, J., 1975. “1/f noise” in music and speech. Nature, 258, 317–318. doi:10.1038/258317a0

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Ellaway, P.H., 1978. Cumulative sum technique and its application to the analysis of peristimulus time histograms. Electroencephalography and Clinical Neurophysiology, 45, 302–304. doi:10.1016/0013-4694(78)90017-2

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Kobayashi, M. and Musha, T., 1982. 1/f fluctuation of heartbeat period. IEEE Transactions on Biomedical Engineering BME, 29, 456–457. doi:10.1109/TBME.1982.324972

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Peng, C.-K., et al., 1992. Long-range correlations in nucleotide sequences. Nature, 356, 168–170. doi:10.1038/356168a0

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Arneodo, A., et al., 1996. Wavelet based fractal analysis of DNA sequences. Physica D: Nonlinear Phenomena, Measures of Spatio-Temporal Dynamics, 96, 291–320. doi:10.1016/0167-2789(96)00029-2

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Leland, W.E., et al., 1993. On the self-similar nature of Ethernet traffic. ACM SIGCOMM Computer Communication Review, 23 (4), 183–193. doi:10.1145/167954

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Frost, V.S. and Melamed, B., 1994. Traffic modelling for telecommunications networks. Communications Magazine, IEEE, 32 (3), 70–81. doi:10.1017/S0022112062000518

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Koutsoyiannis, D., 2003. Climate change, the Hurst phenomenon, and hydrological statistics. Hydrological Sciences Journal, 48, 3–24. doi:10.1623/hysj.48.1.3.43481

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Cohn, T.A. and Lins, H.F., 2005. Nature’s style: naturally trendy. Geophysical Researcher Letters, 32 (L23402). doi:10.1029/2005GL024476

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Hurst, H.E., 1951. Long-term storage capacity of reservoirs. Transactions of the American Social Civil Engineering, 116, 770–808.

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