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On periodicity in series of related terms
Open accessAbstract
An important extension of our ideas regarding periodicity was made in 1927 when Yule pointed out that, instead of regarding a series of annual sunspot numbers as consisting merely of a harmonic series to which a series of random terms were added, we might suppose a certain amount of causal relationship between the successive annual numbers. In that case the system might be regarded as a physical system possessing one or more natural oscillations of its own, all subject to damping; and the effect of annual random disturbances would be to produce a fairly smooth curve with periods varying in amplitude and length, essentially as the sunspot numbers vary. If we call the departures from their mean of our series u1, u2.., Yule showed that the consequence of a single natural period is an equation like ux = kux-1 - ux-2 + vx, where vx represents the “accidental” external “disturbance”; and if there are two natural periods, ux = k1 (ux-1 + ux-3) - k2ux-2 - ux-4 + vx
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Cited by
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Kay, S. M., & Marple, S. L. (1981) · Proceedings of the IEEE · doi:10.1109/proc.1981.12184 · Cited by 3,146
Troup, A. J. (1965) · Quarterly Journal of the Royal Meteorological Society · doi:10.1002/qj.49709139009 · Cited by 769
Omondi, P., Ogallo, L. A., Anyah, R., Muthama, J. M., & Ininda, J. (2013) · International Journal of Climatology · doi:10.1002/joc.3578 · Cited by 60
A comparative simulation study of AR(1) estimators in short time series
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Multivariable time series forecasting using model fusion
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Metadata
- Authors
- Walker, G. T.
- Venue
- Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character
- Publisher
- The Royal Society
- Published
- 1931-06-03
- Volume
- 131
- Issue
- 818
- Pages
- 518-532
- ISSN
- 0950-1207 (ISSN-L)
- 2053-9150
- OpenAlex
- W1983662669
- Cited by
- 381
- References
- 0
- FWCI
- 1.97
- Type
- journal article
- Language
- en
- Open access
- diamond
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- Walker, G. T. (1931). On periodicity in series of related terms. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. https://doi.org/10.1098/rspa.1931.0069
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