Secular variation

The secular variation of a time series is its long-term non-periodic variation (see Decomposition of time series). Whether something is perceived as a secular variation or not depends on the available timescale: a secular variation over a time scale of centuries may be part of a periodic variation over a time scale of millions of years. Natural quantities often have both periodic and secular variations. Secular variation is sometimes called secular trend or secular drift when the emphasis is on a linear long-term trend.

The term secular variation is used wherever time series are applicable in economics, operations research, biological anthropology, astronomy (particularly celestial mechanics) such as VSOP (planets) etc.


In astronomy, secular variations are contrasted with periodic phenomena. In particular, astronomical ephemerides use secular to label the longest-lasting or non-oscillatory perturbations in the motion of planets, as opposed to periodic perturbations which exhibit repetition over the course of a time frame of interest. Solar System ephemerides are essential for the navigation of spacecraft and for all kinds of space observations of the planets, their natural satellites, stars and galaxies.

Most of the known perturbations to motion in stable, regular, and well-determined dynamical systems tend to be periodic at some level, but in many-body systems, chaotic dynamics result in some effects which are one-way (for example, planetary migration).

In the Solar System

Secular phenomena create variations in the orbits of the Moon and the planets. The solar emission spectrum and the solar wind are undergoing secular trends due to migration through the galactic plane, leading to effects that may impact on climate and cause extinction events.


The secular acceleration of the Moon depends on tidal forces. It was discovered early but it was some time before it was correctly explained.[1]


Depending on what time frames are considered, perturbations can appear secular even if they are actually periodic. An example of this is the precession of the Earth's axis considered over the time frame of a few hundred or thousand years. When viewed in this time frame the so-called "precession of the equinoxes" can appear to mimic a secular phenomenon since the axial precession takes 25,771.5 years and monitoring it over a much smaller timeframe appears to simply result in a "drift" of the position of the equinox in the plane of the ecliptic of approximately one degree every 71.6 years,[2] influencing the Milankovitch cycles.[3]

The planets

Secular variation also refers to long-term trends in the orbits of the planets Mercury to Neptune. Several attempts have from time to time been undertaken to analyze and predict such gravitational deviations from ordinary satellite orbits. Others are often referred to as post keplerian effects.

Variations Séculaires des Orbites Planétaires (VSOP) is a modern numerical model[4] that tries to address the problem.

Market trends

Market trends are classified as secular, primary and secondary for long, medium and short time frames.[5] Some traders identify market trends using technical analysis.

Geomagnetic secular variation

Geomagnetic secular variation refers to changes in the Earth's magnetic field. The field has variations on time scales from milliseconds to millions of years, but rapid changes mostly come from currents in the ionosphere and magnetosphere. The secular variation is the changes over periods of a year or more, reflecting changes in the Earth's core. Phenomena associated with this secular variation include geomagnetic jerk, westward drift and geomagnetic reversals.[6]

Biological anthropology

A secular trend has been observed in the age of onset of puberty (menarche/first menstruation and beginning of breast development) of girls around the world beginning roughly 4 months earlier each decade. This is largely believed to be caused by nutritional changes in children over time.[7][8][9][10][11][12]


  1. Jyri B. Kolesnik; Revision of the tidal acceleration of the Moon and the tidal deceleration of the Earth's rotation from historical optical observations of planets, in ISBN 2-901057-45-4 (2001) pp. 231 - 234.
  2. Lowrie, William (2004). Fundamentals of Geophysics. Cambridge University Press. ISBN 0-521-46164-2.
  3. Jurij B. Kolesnik; A new approach to interpretation of the non-precessional equinox motion, in Journées 2000 - systèmes de référence spatio-temporels. J2000, a fundamental epoch for origins of reference systems and astronomical models, Paris, Septembre 2000, edited by N. Capitaine, Observatoire de Paris (2001), pp. 119 – 120. ISBN 2-901057-45-4
  4. Bretagnon, P. (1982). "Théorie du mouvement de l'ensemble des planètes. Solution VSOP82". Astronomy & Astrophysics. 114: 278–288. Bibcode:1982A&A...114..278B.
  5. Edwards, R.; McGee, J.; Bessetti, W. H. C. (2007). Technical Analysis of Stock Trends. CRC Press. p. 17. ISBN 978-0-8493-3772-7.
  6. Merrill, Ronald T.; McElhinny, Michael W.; McFadden, Phillip L. (1996). The Magnetic Field of the Earth: Paleomagnetism, the Core, and the Deep Mantle. International Geophysics Series. 63. Academic Press. ISBN 9780124912458.
  7. Okasha, M; McCarron, P; McEwen, J; Smith, GD (2001). "Age at menarche: secular trends and association with adult anthropometric measures". Annals of Human Biology. 28 (1): 68–78. doi:10.1080/03014460150201896. PMID 11201332.
  8. Wattigney, WA; Srinivasan, SR; Chen, W; Greenlund, KJ; Berenson, GS (1999). "Secular trend of earlier onset of menarche with increasing obesity in black and white girls: the Bogalusa Heart Study". Ethnicity & Disease. 9 (2): 181–189. PMID 10421080.
  9. Prentice, S; Fulford, AJ; Jarjou, LM; Goldberg, GR; Prentice, A (2010). "Evidence for a downward secular trend in age of menarche in a rural Gambian population". Annals of Human Biology. 37 (5): 717–721. doi:10.3109/03014461003727606. PMID 20465526.
  10. Rokade, Shrikant; Mane, Arati (2008), "A Study Of Age At Menarche, The Secular Trend And Factors Associated With It", The Internet Journal of Biological Anthropology, 3 (2), doi:10.5580/115b
  11. Biro, Frank; Galvez, MP; Greenspan, LC; Succop, PA; Vangeepuram, N (Sep 2010), "Pubertal assessment method and baseline characteristics in a mixed longitudinal study of girls", Pediatrics, 126 (3): e583–90, doi:10.1542/peds.2009-3079, PMID 20696727
  12. Euling, Susan; Herman-Giddens, Marcia; Lee, Peter; Selevan, Sherry (February 2008). "Examination of US Puberty-Timing Data from 1940 to 1994 for Secular Trends: Panel Findings". Pediatrics. 121 (3).
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