The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
Some long‐run properties of geophysical records
Abstract
A variety of geophysical records are examined to determine the dependence upon the lag s of a quantity called ‘rescaled range,’ denoted by R(t, s)/S(t, s). If there had been no appreciable dependence between two values of the record at very distant points in time, the ratio R/S would have been proportional to s0.5. But, in fact, as first noted by Edwin Hurst, the R/S ratio of hydrological and other geophysical records is proportional to s H with H ≠ 0.5. Hurst's original claims must be tightened and hedged, and his estimates of H must be discarded, but his general idea will be shown to be correct. We have shown elsewhere that this behavior of R/S means that the strength of long‐range statistical dependence in geophysical records is considerable.
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Cites
Fractional Brownian Motions, Fractional Noises and Applications
Mandelbrot, B. B., & Van Ness, J. W. (1968) · SIAM Review · doi:10.1137/1010093 · Cited by 7,645
Self-citationLong-Term Storage Capacity of Reservoirs
Hurst, H. E. (1951) · Transactions of the American Society of Civil Engineers · doi:10.1061/taceat.0006518 · Cited by 6,212
How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension
Mandelbrot, B. (1967) · Science · doi:10.1126/science.156.3775.636 · Cited by 4,090
Self-citationNoah, Joseph, and Operational Hydrology
Mandelbrot, B. B., & Wallis, J. R. (1968) · Water Resources Research · doi:10.1029/wr004i005p00909 · Cited by 1,117
Self-citationRobustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence
Mandelbrot, B. B., & Wallis, J. R. (1969) · Water Resources Research · doi:10.1029/wr005i005p00967 · Cited by 1,063
Self-citationLong-Term Storage: An Experimental Study.
Lloyd, E. H., Hurst, H. E., Black, R. P., & Simaika, Y. M. (1966) · Journal of the Royal Statistical Society. Series A (General) · doi:10.2307/2982267 · Cited by 766
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Spectral Analysis of Economic Time Series
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New methods in statistical economics
Mandelbrot, B. B. (1997) · Fractals and Scaling in Finance · doi:10.1007/978-1-4757-2763-0_3 · Cited by 434
Self-citationDendroclimatic Changes in Semiarid America
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Cited by
Keshner, M. S. (1982) · Proceedings of the IEEE · doi:10.1109/proc.1982.12282 · Cited by 759
Self-organization of cognitive performance.
Van Orden, G. C., Holden, J. G., & Turvey, M. T. (2003) · Journal of Experimental Psychology: General · doi:10.1037/0096-3445.132.3.331 · Cited by 718
Stock market prices and long-range dependence
Willinger, W., Taqqu, M. S., & Teverovsky, V. (1999) · Finance and Stochastics · doi:10.1007/s007800050049 · Cited by 373
The synthesis and rendering of eroded fractal terrains
Musgrave, F. K., Kolb, C. E., & Mace, R. S. (1989) · Proceedings of the 16th annual conference on Computer graphics and interactive techniques · doi:10.1145/74333.74337 · Cited by 321
Metadata
- Authors
- Mandelbrot, B. B., & Wallis, J. R.
- Venue
- Water Resources Research
- Publisher
- American Geophysical Union (AGU)
- Published
- 1969-04
- Volume
- 5
- Issue
- 2
- Pages
- 321-340
- ISSN
- 0043-1397 (ISSN-L)
- 1944-7973
- OpenAlex
- W2051347137
- Cited by
- 991
- References
- 13
- FWCI
- 63.35
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
